Math 111 - Oct 28, 2011

5.1 Inverse functions...

A relation is any set of ordered pairs or equation with x&y...

Learn Math Graph:400 400 -7.0 1.0 7.0 -7.0 1.0 7.0 g true Function 2.45 1.505 false ((\2\,\1)) Function -4.095 2.135 false ((\-\1\,\1)) Function -0.595 0.77 false ((\1\,\1)) Function 5.04 2.765 false ((\5\,\3)) Function -1.085 2.1000001 false ((\1\,\1)) Color red Function 1.225 3.045 false ((\1\,\2)) Color red Function 1.085 -1.4 false ((\1\,\-\1)) Color red Function 3.0 5.0 false ((\3\,\5)) Color red

Learn Math Graph:400 400 -7.0 1.0 7.0 -7.0 1.0 7.0 g true Function -5.215 2.9750001 false (/\x(^\2)^\y,/\x\-\y)/\=\x(^\2)^\-\y Function 0.7 -1.085 false (/\y(^\2)^\x,/\y\-\x)/\=\y(^\2)^\-\x Color red

Learn Math Graph:400 400 -7.0 1.0 7.0 -7.0 1.0 7.0 g true Function -1.645 4.97 false \y\=\x(^\2)^ Point 0.0 0.0 Point 1.0 1.0 Point 2.0 4.0 Point -2.0 4.0 Point -1.0 1.0 Point 0.0 0.0 Color red Point 1.0 1.0 Color red Point 4.0 2.0 Color red Point 1.0 -1.0 Color red Point 4.0 -2.0 Color red Function 1.015 1.015 false \x\=\y(^\2)^ Color red

An inverse of a relation switches the x&y. See red above.

Remember that a function is a relation that doesn't have repeated x values.

You can tell it's a function if it passes the vertical line test.

It's inverse will be a function if the original passes the horizontal line test.

A function that also passes the horizontal line test - (so its inverse will be a function) is called "one-to-one".

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0.98 0.94500005 0.98 0.94500005 0.98 Color red Freehand 10 0.94500005 0.94500005 1.015 0.94500005 1.015 0.94500005 1.0500001 0.98 1.0500001 0.98 1.085 0.98 1.12 1.015 1.1550001 1.0500001 1.19 1.0500001 1.19 1.0500001 Color red Freehand 16 1.12 1.085 1.1550001 1.085 1.19 1.12 1.225 1.12 1.26 1.12 1.2950001 1.1550001 1.4 1.19 1.505 1.26 1.5749999 1.2950001 1.61 1.3299999 1.68 1.3299999 1.715 1.365 1.75 1.4 1.785 1.4 1.785 1.4 1.785 1.4 Color red Freehand 24 1.645 1.2950001 1.68 1.2950001 1.715 1.2950001 1.715 1.3299999 1.75 1.3299999 1.785 1.365 1.8199999 1.365 1.8549999 1.4 1.8900001 1.435 1.96 1.435 1.995 1.4699999 2.03 1.4699999 2.1000001 1.4699999 2.135 1.505 2.17 1.505 2.24 1.505 2.2749999 1.505 2.345 1.54 2.38 1.54 2.45 1.54 2.52 1.54 2.555 1.54 2.625 1.5749999 2.625 1.5749999 Color red Freehand 24 2.695 1.54 2.73 1.54 2.765 1.54 2.8 1.54 2.835 1.5749999 2.87 1.5749999 2.9399998 1.5749999 3.01 1.61 3.045 1.61 3.1850002 1.645 3.36 1.645 3.43 1.68 3.5 1.68 3.605 1.68 3.6749997 1.715 3.7450001 1.715 3.8500001 1.75 3.92 1.75 4.095 1.785 4.165 1.785 4.235 1.8199999 4.27 1.8199999 4.34 1.8199999 4.34 1.8199999 Color red Freehand 31 4.27 1.785 4.34 1.785 4.375 1.785 4.41 1.785 4.4449997 1.8199999 4.515 1.8199999 4.585 1.8199999 4.6200004 1.8199999 4.69 1.8199999 4.76 1.8549999 4.865 1.8549999 4.935 1.8549999 5.0049996 1.8549999 5.11 1.8549999 5.1800003 1.8900001 5.25 1.8900001 5.355 1.8900001 5.4249997 1.8900001 5.565 1.9250001 5.6 1.9250001 5.635 1.9250001 5.705 1.9250001 5.74 1.9250001 5.74 1.9250001 5.775 1.9250001 5.81 1.9250001 5.81 1.9250001 5.81 1.9250001 5.845 1.9250001 5.845 1.9250001 5.845 1.9250001 Color red Freehand 22 5.4950004 2.17 5.565 2.135 5.6 2.135 5.635 2.135 5.67 2.1000001 5.74 2.0649998 5.775 2.0649998 5.845 2.03 5.8799996 1.995 5.9500003 1.96 6.02 1.9250001 6.02 1.8900001 6.02 1.8900001 6.02 1.8549999 5.915 1.8199999 5.8799996 1.785 5.81 1.75 5.74 1.715 5.705 1.68 5.67 1.645 5.635 1.61 5.635 1.61 Color red Freehand 16 0.07 -0.035 0.035 -0.07 0.035 -0.105 0.035 -0.175 0.0 -0.21 0.0 -0.245 0.0 -0.28 0.0 -0.28 -0.035 -0.315 -0.035 -0.315 -0.035 -0.35 -0.035 -0.35 -0.035 -0.35 -0.035 -0.35 -0.07 -0.385 -0.07 -0.385 Color red Freehand 21 -0.07 -0.245 -0.07 -0.28 -0.07 -0.315 -0.07 -0.315 -0.07 -0.315 -0.07 -0.35 -0.105 -0.35 -0.14 -0.42 -0.175 -0.45499998 -0.175 -0.49 -0.175 -0.52500004 -0.21 -0.52500004 -0.245 -0.56 -0.245 -0.595 -0.245 -0.595 -0.245 -0.595 -0.28 -0.63 -0.28 -0.63 -0.28 -0.63 -0.28 -0.63 -0.28 -0.63 Color red Freehand 18 -0.385 -0.595 -0.42 -0.63 -0.45499998 -0.66499996 -0.49 -0.7 -0.52500004 -0.73499995 -0.56 -0.73499995 -0.595 -0.73499995 -0.595 -0.77 -0.63 -0.77 -0.63 -0.77 -0.66499996 -0.77 -0.66499996 -0.77 -0.66499996 -0.805 -0.66499996 -0.805 -0.66499996 -0.805 -0.66499996 -0.805 -0.66499996 -0.805 -0.66499996 -0.805 Color red Freehand 28 -0.875 -1.015 -0.84 -0.98 -0.805 -0.98 -0.77 -0.94500005 -0.73499995 -0.90999997 -0.7 -0.90999997 -0.66499996 -0.875 -0.595 -0.84 -0.56 -0.805 -0.49 -0.73499995 -0.42 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28 -5.3199997 -1.75 -5.285 -1.715 -5.285 -1.68 -5.3199997 -1.68 -5.3199997 -1.68 -5.3199997 -1.68 -5.355 -1.68 -5.39 -1.68 -5.4249997 -1.68 -5.46 -1.68 -5.4950004 -1.715 -5.53 -1.715 -5.6 -1.75 -5.635 -1.785 -5.775 -1.8549999 -5.845 -1.8900001 -5.845 -1.8900001 -5.8799996 -1.9250001 -5.845 -1.9250001 -5.845 -1.96 -5.74 -1.96 -5.705 -1.995 -5.67 -1.995 -5.635 -2.03 -5.6 -2.03 -5.565 -2.03 -5.53 -2.0649998 -5.53 -2.0649998 Color red

If a function is one-to-one its inverse is also a one-to-one function and we can usually "find" it algebraically....

Learn Math Equation: y =(/ x - 3,/ x + 2)/ has a domain of Learn Math Equation: xs= - 2 has a range Learn Math Equation: ys= 1

Learn Math Graph:400 400 -14.0 1.0 14.0 -14.0 1.0 14.0 g true Function 0.98 3.045 false (/\x\-\3,/\x\+\2)/ Color red Freehand 2 1.26 0.28 1.26 0.28 Color red Freehand 2 1.26 0.28 1.26 0.28 Color red Function 0.94500005 -2.17 false (/\-\3\-\2\x,/\x\-\1)/ Color blue

It's inverse is: Learn Math Equation: x =(/ y - 3,/ y + 2)/ since this is one-to-one: we can solve it for y.

Learn Math Equation: x(( y + 2)) = y - 3

Learn Math Equation: x y + 2 x = y - 3

Learn Math Equation: x y - y = - 3 - 2 x

Learn Math Equation: y(( x - 1)) = - 3 - 2 x

Learn Math Equation: y =(/ - 3 - 2 x,/ x - 1)/ has a range of Learn Math Equation: ys= - 2 has a domain Learn Math Equation: xs= 1

Because we just swapped x and y...

The domain of the original is the range of the inverse

The range of the original is the domain of the inverse

Another:

Learn Math Equation: y =(r,r 2 x - 3)r has a domain Learn Math Equation: 2 x - 3s> 0 which is Learn Math Equation: xs>(/ 3,/ 2)/ it has range: Learn Math Equation: ys> 0

Learn Math Graph:400 400 -7.0 1.0 7.0 -7.0 1.0 7.0 g true Function 3.8500001 1.8549999 false (r,r\2\x\-\3)r Color blue Function -5.25 4.025 false (/\1,/\2)/\x(^\2)^\+(/\3,/\2)/ Freehand 10 0.14 1.505 0.105 1.5749999 0.105 1.5749999 0.105 1.5749999 0.105 1.5749999 0.105 1.5749999 0.105 1.5749999 0.07 1.54 0.07 1.54 0.07 1.54 Color red Freehand 17 0.0 1.54 0.035 1.54 0.035 1.54 0.035 1.54 0.07 1.54 0.07 1.54 0.105 1.54 0.105 1.54 0.14 1.54 0.175 1.54 0.315 1.5749999 0.385 1.5749999 0.385 1.5749999 0.42 1.5749999 0.42 1.5749999 0.45499998 1.61 0.45499998 1.61 Color red Freehand 16 0.385 1.5749999 0.385 1.54 0.385 1.54 0.42 1.54 0.42 1.54 0.45499998 1.5749999 0.49 1.5749999 0.52500004 1.61 0.56 1.645 0.73499995 1.75 0.77 1.785 0.805 1.785 0.875 1.8549999 0.875 1.8549999 0.90999997 1.8900001 0.90999997 1.8900001 Color red Freehand 8 0.98 1.96 1.015 1.96 1.12 2.0649998 1.225 2.205 1.26 2.24 1.2950001 2.3100002 1.4 2.52 1.4 2.52 Color red Freehand 11 1.435 2.6599998 1.4699999 2.695 1.54 2.8 1.5749999 2.87 1.61 2.905 1.61 2.9399998 1.645 2.9750001 1.645 3.01 1.68 3.08 1.75 3.22 1.75 3.22 Color red Freehand 11 1.715 3.255 1.785 3.255 1.8199999 3.36 1.8900001 3.4650002 1.96 3.57 1.995 3.6399999 1.995 3.6749997 2.0649998 3.815 2.135 4.025 2.17 4.1299996 2.17 4.1299996 Color red Freehand 14 2.17 4.235 2.205 4.27 2.24 4.3050003 2.2749999 4.41 2.3100002 4.4449997 2.3100002 4.48 2.345 4.515 2.38 4.585 2.45 4.725 2.485 4.935 2.52 4.97 2.52 5.0049996 2.52 5.0049996 2.52 5.0049996 Color red Freehand 13 2.415 4.865 2.45 4.9 2.485 4.97 2.485 5.0049996 2.52 5.0750003 2.555 5.11 2.555 5.1800003 2.5900002 5.215 2.625 5.285 2.8 5.705 2.835 5.74 2.87 5.845 2.87 5.845 Color red Freehand 11 3.1499999 6.65 3.08 6.44 3.01 6.265 2.9399998 6.09 2.905 6.02 2.87 5.9500003 2.87 5.915 2.835 5.845 2.8 5.74 2.8 5.705 2.8 5.705 Color red Freehand 4 3.08 6.1949997 2.73 5.3199997 2.73 5.25 2.73 5.25 Color red Freehand 36 -3.22 6.685 -3.08 6.7549996 -2.9750001 6.8250003 -2.9750001 6.8250003 -3.01 6.79 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3.43 -1.995 3.36 -2.03 3.22 -2.0649998 3.1499999 -2.0649998 3.115 -1.995 3.045 -1.995 3.045 Color red Freehand 10 -1.645 3.1499999 -1.8199999 2.905 -1.8549999 2.87 -1.8900001 2.8 -1.8900001 2.73 -1.9250001 2.6599998 -1.9250001 2.625 -1.8900001 2.555 -1.75 2.5900002 -1.75 2.5900002 Color red Freehand 10 -1.435 2.87 -1.4 2.9399998 -1.435 2.9399998 -1.505 2.835 -1.54 2.765 -1.68 2.345 -1.68 2.17 -1.68 2.135 -1.54 2.1000001 -1.54 2.1000001 Color red Freehand 12 -0.94500005 2.625 -0.90999997 2.695 -0.94500005 2.695 -1.085 2.415 -1.1550001 2.24 -1.19 2.03 -1.19 1.96 -1.19 1.8549999 -1.19 1.785 -1.12 1.75 -1.015 1.8199999 -1.015 1.8199999 Color red Freehand 5 -0.73499995 2.345 -0.84 1.75 -0.805 1.61 -0.805 1.54 -0.805 1.54 Color red Freehand 39 0.07 1.645 0.105 1.5749999 0.07 1.54 0.07 1.505 0.035 1.435 0.035 1.435 0.0 1.4 -0.035 1.4 -0.035 1.4699999 0.0 1.505 0.035 1.5749999 0.07 1.61 0.105 1.645 0.105 1.54 0.07 1.505 0.035 1.4699999 0.0 1.4 -0.07 1.365 -0.07 1.435 -0.07 1.4699999 -0.035 1.505 -0.035 1.54 0.035 1.54 0.035 1.4699999 0.0 1.4 -0.035 1.365 -0.07 1.3299999 -0.14 1.435 -0.14 1.505 -0.14 1.5749999 -0.105 1.61 -0.07 1.61 0.0 1.5749999 0.0 1.505 0.0 1.4699999 0.0 1.365 -0.105 1.5749999 -0.105 1.5749999 -0.105 1.5749999 Color red Freehand 11 -0.07 0.07 -0.07 0.0 -0.07 -0.105 -0.035 -0.14 -0.035 -0.21 0.0 -0.315 0.0 -0.35 0.0 -0.35 0.0 -0.385 0.0 -0.35 0.0 -0.35 Color red Freehand 12 -0.105 0.14 -0.07 0.28 -0.07 0.28 -0.07 0.28 -0.07 0.245 -0.07 0.175 -0.07 0.105 0.0 -0.42 0.0 -0.52500004 0.0 -0.56 0.0 -0.595 0.0 -0.595 Color red Freehand 12 0.56 -0.385 0.56 -0.45499998 0.595 -0.49 0.73499995 -0.52500004 0.90999997 -0.52500004 1.1550001 -0.45499998 1.2950001 -0.45499998 2.03 -0.42 2.205 -0.42 2.2749999 -0.42 2.3100002 -0.385 2.3100002 -0.385 Color red Freehand 12 1.995 -0.28 2.0649998 -0.28 2.1000001 -0.315 2.17 -0.35 2.24 -0.35 2.2749999 -0.385 2.3100002 -0.45499998 2.205 -0.63 2.0649998 -0.73499995 2.03 -0.805 1.995 -0.805 1.995 -0.805 Color red Freehand 64 0.0 1.3299999 0.07 1.365 0.07 1.4 0.105 1.4 0.175 1.4699999 0.21 1.505 0.245 1.505 0.385 1.5749999 0.45499998 1.61 0.52500004 1.61 0.56 1.645 0.595 1.645 0.63 1.68 0.66499996 1.68 0.94500005 1.9250001 1.015 2.03 1.0500001 2.0649998 1.12 2.135 1.4 2.45 1.4699999 2.5900002 1.505 2.6599998 1.54 2.6599998 1.54 2.695 1.645 2.87 1.715 2.9750001 1.75 3.045 1.8199999 3.115 1.8549999 3.1850002 1.8549999 3.22 1.995 3.5349998 2.0649998 3.6399999 2.135 3.7450001 2.135 3.7800002 2.17 3.815 2.205 3.92 2.3100002 4.1299996 2.38 4.2000003 2.415 4.27 2.45 4.34 2.485 4.4449997 2.52 4.48 2.6599998 4.725 2.73 4.795 2.73 4.83 2.765 4.865 2.765 4.935 2.8 5.0049996 2.835 5.0750003 2.9399998 5.4950004 2.9750001 5.6 3.01 5.67 3.01 5.74 3.045 5.915 3.08 6.125 3.115 6.23 3.115 6.265 3.115 6.335 3.1499999 6.405 3.1850002 6.545 3.255 6.685 3.29 6.72 3.29 6.7549996 3.29 7.035 3.29 7.035 Color red

The inverse function is:

Learn Math Equation: x =(r,r 2 y - 3)r

Learn Math Equation: x(^ 2)^ = 2 y - 3

Learn Math Equation: x(^ 2)^ + 3 = 2 y

Learn Math Equation: y =(/ 1,/ 2)/ x(^ 2)^ +(/ 3,/ 2)/ sorta

more precisely Learn Math Equation: y =(/ 1,/ 2)/ x(^ 2)^ +(/ 3,/ 2)/ , xs> 0 I tacked a domain of Learn Math Equation: xs> 0 "by hand" and it has a range Learn Math Equation: ys>(/ 3,/ 2)/

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5.0750003 3.115 5.04 3.115 5.0049996 3.08 4.97 3.045 4.935 3.045 4.9 3.01 4.865 2.9750001 4.865 2.905 4.865 2.87 4.865 2.87 4.9 2.87 4.97 2.87 5.0049996 2.87 5.0750003 2.905 5.11 2.9399998 5.145 2.9399998 5.145 2.9750001 5.145 2.9750001 5.145 3.01 5.145 3.01 5.145 Color red Freehand 52 -0.98 3.92 -0.98 3.885 -1.015 3.8500001 -1.015 3.8500001 -1.015 3.815 -1.0500001 3.815 -1.0500001 3.815 -1.0500001 3.815 -1.085 3.815 -1.085 3.815 -1.12 3.8500001 -1.12 3.885 -1.12 3.885 -1.12 3.92 -1.12 3.955 -1.12 3.99 -1.12 4.025 -1.12 4.06 -1.12 4.06 -1.12 4.095 -1.085 4.095 -1.085 4.095 -1.085 4.095 -1.0500001 4.095 -1.0500001 4.095 -1.015 4.095 -1.015 4.06 -0.98 4.025 -0.98 3.99 -0.98 3.955 -0.98 3.92 -0.98 3.885 -0.98 3.885 -0.98 3.8500001 -1.015 3.815 -1.0500001 3.815 -1.0500001 3.815 -1.085 3.7800002 -1.12 3.7800002 -1.1550001 3.8500001 -1.19 3.8500001 -1.19 3.92 -1.19 3.99 -1.1550001 4.06 -1.1550001 4.095 -1.12 4.1299996 -1.12 4.165 -1.085 4.165 -1.085 4.165 -1.0500001 4.165 -1.0500001 4.1299996 -1.0500001 4.1299996 Color red Freehand 35 -3.255 4.585 -3.22 4.6200004 -3.22 4.655 -3.255 4.655 -3.255 4.69 -3.29 4.69 -3.29 4.725 -3.325 4.725 -3.325 4.725 -3.36 4.725 -3.36 4.725 -3.395 4.725 -3.43 4.725 -3.4650002 4.69 -3.5 4.655 -3.5349998 4.655 -3.5349998 4.6200004 -3.57 4.5499997 -3.605 4.515 -3.605 4.4449997 -3.605 4.375 -3.605 4.34 -3.605 4.27 -3.57 4.2000003 -3.5349998 4.095 -3.5349998 4.025 -3.5 3.955 -3.4650002 3.885 -3.43 3.8500001 -3.43 3.7800002 -3.395 3.7450001 -3.395 3.7099998 -3.395 3.6749997 -3.395 3.6399999 -3.395 3.6399999 Color red Freehand 12 -3.6749997 3.99 -3.605 3.99 -3.605 3.99 -3.57 3.99 -3.5349998 3.99 -3.5 3.99 -3.43 3.99 -3.395 3.99 -3.29 4.025 -3.255 4.025 -3.1850002 4.06 -3.1850002 4.06 Color red Freehand 18 -2.6599998 5.04 -2.6599998 5.0049996 -2.6599998 4.97 -2.695 4.935 -2.695 4.9 -2.73 4.865 -2.73 4.795 -2.765 4.69 -2.765 4.6200004 -2.765 4.515 -2.8 4.4449997 -2.8 4.235 -2.765 4.165 -2.765 4.095 -2.73 4.06 -2.695 4.025 -2.6599998 3.99 -2.6599998 3.99 Color red Freehand 15 -1.9250001 5.04 -1.96 4.97 -1.995 4.9 -2.03 4.865 -2.0649998 4.795 -2.1000001 4.76 -2.135 4.69 -2.17 4.6200004 -2.205 4.5499997 -2.24 4.48 -2.2749999 4.4449997 -2.2749999 4.41 -2.3100002 4.375 -2.345 4.34 -2.345 4.34 Color red Freehand 16 -2.38 4.76 -2.3100002 4.76 -2.2749999 4.725 -2.2749999 4.725 -2.2749999 4.69 -2.24 4.655 -2.24 4.6200004 -2.205 4.585 -2.17 4.515 -2.135 4.4449997 -2.1000001 4.41 -2.0649998 4.375 -2.03 4.34 -1.995 4.34 -1.995 4.34 -1.995 4.34 Color red Freehand 25 -2.03 5.635 -1.995 5.635 -1.96 5.635 -1.96 5.6 -1.9250001 5.6 -1.9250001 5.565 -1.8900001 5.53 -1.8549999 5.4950004 -1.8199999 5.4249997 -1.785 5.39 -1.75 5.3199997 -1.68 5.285 -1.645 5.215 -1.645 5.145 -1.61 5.0750003 -1.61 4.935 -1.61 4.865 -1.61 4.83 -1.645 4.76 -1.645 4.725 -1.715 4.6200004 -1.715 4.6200004 -1.75 4.585 -1.785 4.585 -1.785 4.585 Color red Freehand 2 3.01 0.49 3.01 0.49 Color blue Freehand 152 1.015 -5.0049996 1.0500001 -5.0750003 1.0500001 -5.0750003 1.015 -5.11 1.015 -5.145 1.015 -5.145 0.98 -5.145 0.98 -5.145 0.98 -5.145 0.94500005 -5.145 0.94500005 -5.11 0.94500005 -5.0750003 0.94500005 -5.0750003 0.94500005 -5.04 0.94500005 -5.0049996 0.94500005 -5.0049996 0.98 -5.0049996 0.98 -5.0049996 0.98 -5.0049996 1.015 -5.0049996 1.015 -5.0049996 1.0500001 -5.0049996 1.0500001 -5.0049996 1.0500001 -5.0049996 1.0500001 -5.0049996 1.0500001 -5.04 1.0500001 -5.0750003 1.0500001 -5.11 1.0500001 -5.145 1.0500001 -5.1800003 1.015 -5.215 1.015 -5.215 0.98 -5.215 0.94500005 -5.215 0.94500005 -5.215 0.90999997 -5.1800003 0.90999997 -5.1800003 0.90999997 -5.145 0.875 -5.11 0.875 -5.04 0.875 -5.0049996 0.875 -5.0049996 0.90999997 -4.935 0.90999997 -4.935 0.94500005 -4.9 0.98 -4.9 0.98 -4.9 0.98 -4.865 1.015 -4.865 1.015 -4.9 1.015 -4.935 1.015 -5.0049996 1.015 -5.0049996 0.98 -5.04 0.98 -5.04 0.98 -5.0750003 0.94500005 -5.0750003 0.94500005 -5.0750003 0.94500005 -5.0750003 0.90999997 -5.0750003 0.90999997 -5.0750003 0.90999997 -5.04 0.875 -5.04 0.875 -5.0049996 0.875 -4.97 0.875 -4.935 0.875 -4.9 0.875 -4.865 0.875 -4.865 0.90999997 -4.83 0.90999997 -4.83 0.94500005 -4.83 0.94500005 -4.83 0.94500005 -4.83 0.98 -4.83 0.98 -4.865 0.98 -4.865 1.015 -4.9 1.015 -4.935 1.015 -4.97 1.015 -5.0049996 1.015 -5.0049996 1.015 -5.04 1.015 -5.0750003 0.98 -5.0750003 0.98 -5.11 0.98 -5.11 0.94500005 -5.11 0.94500005 -5.11 0.94500005 -5.11 0.90999997 -5.11 0.90999997 -5.0750003 0.90999997 -5.0750003 0.90999997 -5.04 0.90999997 -5.0049996 0.90999997 -4.97 0.90999997 -4.935 0.90999997 -4.935 0.90999997 -4.9 0.94500005 -4.865 0.94500005 -4.83 0.94500005 -4.83 0.98 -4.83 0.98 -4.83 1.015 -4.83 1.015 -4.83 1.0500001 -4.83 1.0500001 -4.83 1.0500001 -4.865 1.0500001 -4.9 1.0500001 -4.935 1.0500001 -4.97 1.0500001 -5.0049996 1.0500001 -5.04 1.0500001 -5.04 1.0500001 -5.0750003 1.015 -5.0750003 1.015 -5.0750003 1.015 -5.0750003 0.98 -5.0750003 0.98 -5.0750003 0.94500005 -5.04 0.94500005 -5.0049996 0.94500005 -4.97 0.94500005 -4.935 0.94500005 -4.935 0.98 -4.865 0.98 -4.865 0.98 -4.83 1.015 -4.83 1.0500001 -4.83 1.0500001 -4.83 1.085 -4.865 1.085 -4.865 1.12 -4.9 1.12 -4.935 1.12 -4.935 1.12 -4.97 1.12 -5.0049996 1.12 -5.0049996 1.085 -5.04 1.085 -5.04 1.0500001 -5.04 1.0500001 -5.04 1.015 -5.04 1.015 -5.04 0.98 -5.04 0.98 -5.0049996 0.98 -4.97 0.98 -4.935 0.98 -4.935 0.98 -4.935 Color blue Freehand 102 1.995 -2.9750001 2.03 -3.01 2.03 -3.045 2.03 -3.045 2.03 -3.045 2.03 -3.08 2.03 -3.08 2.03 -3.08 2.03 -3.115 2.03 -3.115 2.03 -3.115 2.03 -3.115 2.03 -3.115 2.03 -3.1499999 1.995 -3.115 1.995 -3.115 1.96 -3.115 1.96 -3.115 1.96 -3.08 1.96 -3.08 1.96 -3.045 1.96 -3.045 1.96 -3.01 1.995 -2.9750001 1.995 -2.9750001 1.995 -2.9750001 1.995 -2.9750001 1.995 -2.9750001 2.03 -2.9750001 2.03 -3.01 2.03 -3.01 2.03 -3.045 2.03 -3.08 2.03 -3.115 2.03 -3.1499999 1.995 -3.1850002 1.96 -3.22 1.96 -3.255 1.96 -3.255 1.9250001 -3.255 1.9250001 -3.255 1.8900001 -3.255 1.8900001 -3.255 1.8900001 -3.22 1.8900001 -3.22 1.8900001 -3.1850002 1.8900001 -3.115 1.8900001 -3.08 1.8900001 -3.045 1.8900001 -3.01 1.9250001 -2.9750001 1.9250001 -2.9399998 1.9250001 -2.9399998 1.96 -2.9399998 1.96 -2.9399998 1.995 -2.9399998 1.995 -2.9399998 2.03 -2.9750001 2.03 -3.01 2.03 -3.045 2.03 -3.08 2.03 -3.115 1.995 -3.115 1.995 -3.1499999 1.995 -3.1499999 1.995 -3.1499999 1.96 -3.1499999 1.96 -3.1499999 1.96 -3.115 1.96 -3.115 1.96 -3.08 1.9250001 -3.08 1.9250001 -3.01 1.9250001 -2.9750001 1.9250001 -2.9399998 1.96 -2.87 1.96 -2.87 1.96 -2.87 1.995 -2.835 1.995 -2.835 2.03 -2.835 2.03 -2.835 2.03 -2.835 2.03 -2.87 2.03 -2.87 2.0649998 -2.9399998 2.03 -2.9750001 2.03 -2.9750001 2.03 -3.01 1.995 -3.01 1.995 -3.045 1.96 -3.045 1.96 -3.045 1.96 -3.045 1.9250001 -3.045 1.9250001 -3.045 1.9250001 -3.01 1.9250001 -2.9750001 1.9250001 -2.9750001 1.9250001 -2.905 1.96 -2.905 1.96 -2.905 Color blue Freehand 151 1.015 -5.04 1.0500001 -5.0049996 1.0500001 -5.0049996 1.0500001 -5.0049996 1.085 -4.97 1.085 -4.97 1.085 -4.97 1.085 -4.935 1.085 -4.935 1.12 -4.9 1.12 -4.9 1.12 -4.9 1.12 -4.865 1.12 -4.83 1.1550001 -4.83 1.1550001 -4.795 1.1550001 -4.795 1.1550001 -4.76 1.19 -4.76 1.19 -4.725 1.19 -4.725 1.19 -4.725 1.19 -4.69 1.19 -4.69 1.225 -4.655 1.225 -4.655 1.225 -4.655 1.225 -4.6200004 1.225 -4.6200004 1.225 -4.6200004 1.26 -4.585 1.26 -4.585 1.26 -4.5499997 1.2950001 -4.5499997 1.2950001 -4.515 1.2950001 -4.515 1.2950001 -4.48 1.2950001 -4.48 1.3299999 -4.48 1.3299999 -4.4449997 1.3299999 -4.4449997 1.3299999 -4.41 1.3299999 -4.41 1.365 -4.375 1.365 -4.375 1.365 -4.34 1.365 -4.34 1.365 -4.3050003 1.365 -4.3050003 1.365 -4.3050003 1.365 -4.27 1.365 -4.27 1.365 -4.235 1.4 -4.235 1.4 -4.235 1.4 -4.2000003 1.4 -4.2000003 1.4 -4.165 1.4 -4.165 1.4 -4.1299996 1.4 -4.095 1.4 -4.095 1.4 -4.095 1.4 -4.06 1.4 -4.06 1.435 -4.025 1.435 -4.025 1.435 -4.025 1.435 -3.99 1.435 -3.99 1.435 -3.955 1.435 -3.955 1.4699999 -3.955 1.4699999 -3.92 1.4699999 -3.92 1.4699999 -3.92 1.4699999 -3.885 1.505 -3.885 1.505 -3.8500001 1.505 -3.815 1.505 -3.815 1.54 -3.7800002 1.54 -3.7800002 1.54 -3.7450001 1.54 -3.7450001 1.54 -3.7099998 1.5749999 -3.7099998 1.5749999 -3.6749997 1.5749999 -3.6749997 1.5749999 -3.6399999 1.5749999 -3.605 1.5749999 -3.605 1.61 -3.57 1.61 -3.57 1.61 -3.5349998 1.61 -3.5 1.645 -3.5 1.645 -3.4650002 1.645 -3.4650002 1.645 -3.43 1.645 -3.43 1.645 -3.43 1.68 -3.395 1.68 -3.395 1.68 -3.395 1.68 -3.36 1.68 -3.36 1.68 -3.36 1.68 -3.36 1.68 -3.325 1.68 -3.325 1.68 -3.29 1.715 -3.29 1.715 -3.29 1.715 -3.255 1.715 -3.255 1.715 -3.22 1.715 -3.22 1.715 -3.22 1.75 -3.1850002 1.75 -3.1850002 1.75 -3.1850002 1.75 -3.1499999 1.75 -3.1499999 1.75 -3.1499999 1.75 -3.1499999 1.75 -3.1499999 1.75 -3.1499999 1.75 -3.115 1.785 -3.115 1.785 -3.115 1.785 -3.08 1.785 -3.08 1.785 -3.08 1.785 -3.08 1.785 -3.08 1.785 -3.045 1.8199999 -3.045 1.8199999 -3.045 1.8199999 -3.045 1.8199999 -3.045 1.8199999 -3.045 1.8199999 -3.01 1.8199999 -3.01 1.8199999 -3.01 1.8199999 -3.01 1.8199999 -3.01 1.8199999 -3.01 1.8199999 -3.01 1.8199999 -3.01 1.8199999 -3.01 Color blue Freehand 43 1.8900001 -3.08 1.8900001 -3.045 1.8900001 -3.045 1.8900001 -3.045 1.8900001 -3.045 1.8900001 -3.01 1.8900001 -3.01 1.8900001 -3.01 1.8900001 -2.9750001 1.8900001 -2.9750001 1.8900001 -2.9399998 1.8900001 -2.9399998 1.9250001 -2.905 1.9250001 -2.905 1.9250001 -2.905 1.9250001 -2.905 1.9250001 -2.905 1.9250001 -2.905 1.9250001 -2.905 1.9250001 -2.905 1.9250001 -2.905 1.9250001 -2.905 1.9250001 -2.9399998 1.8900001 -2.9399998 1.8900001 -2.9750001 1.8900001 -3.01 1.8900001 -3.045 1.8900001 -3.08 1.8900001 -3.115 1.8549999 -3.1499999 1.8549999 -3.1850002 1.8199999 -3.255 1.785 -3.36 1.785 -3.395 1.75 -3.4650002 1.715 -3.57 1.68 -3.605 1.68 -3.6399999 1.645 -3.6749997 1.645 -3.7099998 1.645 -3.7099998 1.645 -3.7450001 1.645 -3.7450001 Color blue Freehand 98 3.955 -1.015 3.92 -1.0500001 3.92 -1.0500001 3.885 -1.0500001 3.885 -1.0500001 3.885 -1.0500001 3.8500001 -1.0500001 3.8500001 -1.0500001 3.8500001 -1.015 3.8500001 -0.98 3.8500001 -0.94500005 3.8500001 -0.90999997 3.8500001 -0.90999997 3.8500001 -0.875 3.885 -0.875 3.885 -0.84 3.885 -0.84 3.92 -0.84 3.92 -0.84 3.955 -0.84 3.955 -0.875 3.955 -0.875 3.955 -0.90999997 3.955 -0.94500005 3.955 -0.98 3.955 -1.015 3.955 -1.0500001 3.955 -1.085 3.955 -1.085 3.92 -1.12 3.92 -1.12 3.92 -1.1550001 3.885 -1.1550001 3.885 -1.1550001 3.8500001 -1.12 3.8500001 -1.12 3.8500001 -1.085 3.8500001 -1.0500001 3.8500001 -1.015 3.8500001 -0.98 3.885 -0.98 3.885 -0.94500005 3.885 -0.94500005 3.92 -0.90999997 3.92 -0.90999997 3.955 -0.90999997 3.955 -0.90999997 3.955 -0.90999997 3.99 -0.90999997 3.99 -0.94500005 3.99 -0.94500005 3.99 -0.98 3.99 -0.98 3.99 -1.015 3.99 -1.0500001 3.955 -1.0500001 3.955 -1.085 3.955 -1.085 3.92 -1.12 3.885 -1.12 3.885 -1.12 3.885 -1.12 3.8500001 -1.12 3.8500001 -1.085 3.815 -1.085 3.815 -1.015 3.8500001 -0.98 3.8500001 -0.94500005 3.885 -0.90999997 3.92 -0.90999997 3.955 -0.90999997 3.955 -0.90999997 3.99 -0.90999997 3.99 -0.90999997 3.99 -0.90999997 4.025 -0.94500005 4.025 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4.6200004 -2.87 4.6200004 -2.87 Color blue Freehand 25 5.04 -2.9399998 5.04 -2.905 5.04 -2.905 5.04 -2.905 5.0049996 -2.905 5.0049996 -2.905 4.97 -2.905 4.935 -2.9750001 4.9 -3.045 4.865 -3.115 4.83 -3.1850002 4.795 -3.255 4.76 -3.36 4.76 -3.4650002 4.725 -3.6399999 4.725 -3.7099998 4.725 -3.815 4.725 -3.8500001 4.795 -3.955 4.795 -3.99 4.865 -4.06 4.935 -4.06 4.97 -4.06 5.0049996 -4.06 5.0049996 -4.06 Color blue Freehand 12 5.6 -3.395 5.53 -3.43 5.53 -3.4650002 5.46 -3.5349998 5.39 -3.6749997 5.355 -3.7450001 5.3199997 -3.7800002 5.25 -3.885 5.215 -3.885 5.215 -3.92 5.1800003 -3.92 5.1800003 -3.92 Color blue Freehand 16 5.215 -3.43 5.285 -3.395 5.285 -3.43 5.285 -3.43 5.3199997 -3.4650002 5.355 -3.5349998 5.39 -3.57 5.4249997 -3.6749997 5.46 -3.7450001 5.4950004 -3.7800002 5.53 -3.815 5.565 -3.8500001 5.565 -3.885 5.6 -3.885 5.6 -3.885 5.6 -3.885 Color blue Freehand 27 5.67 -2.9399998 5.67 -2.905 5.67 -2.87 5.67 -2.87 5.67 -2.87 5.705 -2.905 5.705 -2.905 5.74 -2.9750001 5.775 -3.01 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-3.885 -1.54 -3.885 -1.54 Color red Freehand 15 -3.255 -1.505 -3.1850002 -1.54 -3.1850002 -1.5749999 -3.1850002 -1.61 -3.1850002 -1.645 -3.1850002 -1.68 -3.1850002 -1.75 -3.1850002 -1.8199999 -3.1850002 -1.8549999 -3.22 -1.9250001 -3.22 -1.96 -3.255 -2.03 -3.255 -2.03 -3.29 -2.0649998 -3.29 -2.0649998 Color red Freehand 52 -2.6599998 -0.98 -2.625 -0.94500005 -2.625 -0.90999997 -2.625 -0.90999997 -2.625 -0.90999997 -2.625 -0.875 -2.625 -0.875 -2.5900002 -0.875 -2.555 -0.84 -2.555 -0.84 -2.45 -0.805 -2.415 -0.805 -2.415 -0.805 -2.38 -0.805 -2.345 -0.84 -2.3100002 -0.875 -2.3100002 -0.90999997 -2.3100002 -0.94500005 -2.3100002 -0.98 -2.3100002 -1.015 -2.3100002 -1.085 -2.38 -1.1550001 -2.38 -1.19 -2.415 -1.225 -2.45 -1.225 -2.485 -1.225 -2.485 -1.225 -2.485 -1.225 -2.485 -1.225 -2.485 -1.225 -2.485 -1.225 -2.485 -1.225 -2.45 -1.225 -2.415 -1.225 -2.38 -1.26 -2.38 -1.26 -2.345 -1.2950001 -2.345 -1.2950001 -2.345 -1.3299999 -2.345 -1.365 -2.345 -1.4 -2.38 -1.435 -2.415 -1.505 -2.45 -1.54 -2.52 -1.54 -2.555 -1.5749999 -2.5900002 -1.5749999 -2.5900002 -1.5749999 -2.5900002 -1.54 -2.5900002 -1.54 -2.5900002 -1.54 -2.5900002 -1.54 Color red Freehand 61 -2.24 -0.56 -2.205 -0.56 -2.17 -0.56 -2.1000001 -0.56 -2.0649998 -0.56 -2.03 -0.56 -1.9250001 -0.56 -1.8900001 -0.595 -1.8549999 -0.595 -1.8199999 -0.595 -1.785 -0.595 -1.785 -0.63 -1.75 -0.63 -1.75 -0.63 -1.75 -0.66499996 -1.75 -0.66499996 -1.75 -0.7 -1.75 -0.73499995 -1.75 -0.805 -1.75 -0.90999997 -1.75 -1.085 -1.75 -1.1550001 -1.75 -1.225 -1.75 -1.2950001 -1.75 -1.435 -1.75 -1.505 -1.715 -1.5749999 -1.715 -1.61 -1.715 -1.68 -1.715 -1.715 -1.68 -1.75 -1.68 -1.785 -1.68 -1.785 -1.68 -1.785 -1.68 -1.785 -1.68 -1.785 -1.68 -1.785 -1.68 -1.785 -1.68 -1.785 -1.715 -1.785 -1.715 -1.785 -1.715 -1.8199999 -1.75 -1.8199999 -1.785 -1.8549999 -1.785 -1.8549999 -1.8199999 -1.8549999 -1.8199999 -1.8549999 -1.8900001 -1.8900001 -1.9250001 -1.8900001 -1.96 -1.8900001 -1.995 -1.8900001 -2.03 -1.8900001 -2.0649998 -1.8900001 -2.1000001 -1.8900001 -2.1000001 -1.8900001 -2.1000001 -1.8900001 -2.1000001 -1.8900001 -2.1000001 -1.8900001 -2.1000001 -1.8900001 -2.0649998 -1.8900001 -2.0649998 -1.8900001 Color red Freehand 64 -6.51 -2.6599998 -6.475 -2.6599998 -6.475 -2.6599998 -6.475 -2.695 -6.475 -2.695 -6.475 -2.765 -6.44 -2.8 -6.44 -2.9399998 -6.44 -3.045 -6.44 -3.1499999 -6.44 -3.22 -6.475 -3.36 -6.475 -3.4650002 -6.475 -3.5 -6.475 -3.5349998 -6.475 -3.5349998 -6.475 -3.5349998 -6.475 -3.5349998 -6.51 -3.4650002 -6.51 -3.325 -6.51 -3.22 -6.51 -3.045 -6.51 -2.9399998 -6.475 -2.765 -6.44 -2.6599998 -6.405 -2.625 -6.3700004 -2.5900002 -6.335 -2.555 -6.2999997 -2.52 -6.265 -2.52 -6.1949997 -2.52 -6.1949997 -2.52 -6.16 -2.5900002 -6.125 -2.6599998 -6.125 -2.695 -6.125 -2.73 -6.16 -2.835 -6.16 -2.905 -6.23 -2.9750001 -6.23 -3.01 -6.265 -3.045 -6.2999997 -3.045 -6.335 -3.08 -6.335 -3.08 -6.335 -3.08 -6.335 -3.08 -6.335 -3.08 -6.335 -3.08 -6.2999997 -3.045 -6.2999997 -3.045 -6.265 -3.08 -6.23 -3.08 -6.23 -3.115 -6.1949997 -3.1499999 -6.16 -3.255 -6.125 -3.325 -6.09 -3.43 -6.09 -3.4650002 -6.0550003 -3.4650002 -6.0550003 -3.5 -6.0550003 -3.5 -6.0550003 -3.5 -6.0550003 -3.5 -6.0550003 -3.5 Color red Freehand 11 -5.985 -2.555 -5.915 -2.555 -5.915 -2.555 -5.915 -2.555 -5.915 -2.555 -5.8799996 -2.555 -5.8799996 -2.5900002 -5.8799996 -2.5900002 -5.8799996 -2.625 -5.845 -2.625 -5.845 -2.625 Color red Freehand 11 -5.74 -3.29 -5.705 -3.36 -5.705 -3.395 -5.74 -3.43 -5.74 -3.5 -5.74 -3.5349998 -5.74 -3.57 -5.74 -3.605 -5.74 -3.605 -5.74 -3.6399999 -5.74 -3.6399999 Color red Freehand 31 -4.935 -2.6599998 -4.97 -2.695 -4.935 -2.73 -4.935 -2.835 -4.935 -2.905 -4.935 -2.9750001 -4.935 -3.08 -4.935 -3.1499999 -4.935 -3.22 -4.935 -3.29 -4.935 -3.43 -4.935 -3.5 -4.935 -3.5349998 -4.935 -3.57 -4.9 -3.6399999 -4.9 -3.6749997 -4.9 -3.6749997 -4.865 -3.7450001 -4.83 -3.7450001 -4.795 -3.7800002 -4.795 -3.7800002 -4.76 -3.815 -4.725 -3.815 -4.655 -3.815 -4.6200004 -3.8500001 -4.5499997 -3.8500001 -4.5499997 -3.8500001 -4.48 -3.8500001 -4.48 -3.8500001 -4.48 -3.815 -4.48 -3.815 Color red Freehand 10 -5.11 -2.87 -5.04 -2.905 -5.0049996 -2.905 -4.935 -2.9399998 -4.865 -2.9399998 -4.83 -2.9399998 -4.795 -2.905 -4.725 -2.905 -4.69 -2.87 -4.69 -2.87 Color red Freehand 16 -4.235 -3.01 -4.2000003 -3.01 -4.2000003 -3.01 -4.2000003 -3.01 -4.2000003 -3.01 -4.165 -3.08 -4.165 -3.1850002 -4.165 -3.255 -4.1299996 -3.395 -4.1299996 -3.4650002 -4.1299996 -3.5349998 -4.1299996 -3.57 -4.1299996 -3.6399999 -4.095 -3.6749997 -4.095 -3.7099998 -4.095 -3.7099998 Color red Freehand 14 -3.6399999 -3.605 -3.57 -3.6749997 -3.5349998 -3.7099998 -3.5349998 -3.7450001 -3.5 -3.815 -3.4650002 -3.885 -3.4650002 -3.99 -3.4650002 -4.06 -3.4650002 -4.1299996 -3.4650002 -4.165 -3.5 -4.2000003 -3.5349998 -4.27 -3.5349998 -4.3050003 -3.5349998 -4.3050003 Color red Freehand 50 -2.87 -2.9750001 -2.8 -2.9399998 -2.8 -2.9399998 -2.765 -2.9399998 -2.765 -2.9399998 -2.73 -2.905 -2.695 -2.905 -2.6599998 -2.87 -2.625 -2.87 -2.5900002 -2.87 -2.5900002 -2.835 -2.5900002 -2.835 -2.5900002 -2.835 -2.625 -2.835 -2.625 -2.835 -2.6599998 -2.87 -2.695 -2.87 -2.73 -2.905 -2.765 -2.905 -2.8 -2.9399998 -2.87 -2.9399998 -2.87 -2.9750001 -2.9399998 -3.01 -2.9399998 -3.01 -2.9750001 -3.045 -2.9750001 -3.045 -2.9750001 -3.08 -2.9750001 -3.115 -2.9750001 -3.115 -2.9750001 -3.1499999 -2.9399998 -3.1499999 -2.905 -3.1499999 -2.87 -3.1850002 -2.87 -3.1850002 -2.8 -3.1850002 -2.765 -3.1850002 -2.765 -3.1850002 -2.73 -3.22 -2.73 -3.255 -2.695 -3.29 -2.695 -3.325 -2.73 -3.36 -2.73 -3.4650002 -2.765 -3.5 -2.8 -3.5349998 -2.8 -3.57 -2.835 -3.57 -2.835 -3.57 -2.87 -3.57 -2.87 -3.57 Color red Freehand 51 -2.345 -2.695 -2.345 -2.6599998 -2.3100002 -2.625 -2.2749999 -2.625 -2.24 -2.625 -2.17 -2.625 -2.135 -2.625 -2.1000001 -2.625 -2.0649998 -2.625 -2.03 -2.6599998 -1.995 -2.695 -1.96 -2.765 -1.96 -2.8 -1.96 -2.835 -1.96 -2.9399998 -1.96 -3.01 -1.96 -3.1499999 -1.96 -3.22 -1.96 -3.29 -1.96 -3.43 -1.96 -3.5 -1.96 -3.605 -1.96 -3.6399999 -1.96 -3.6749997 -1.96 -3.7099998 -1.96 -3.7450001 -1.96 -3.7450001 -1.96 -3.7450001 -1.96 -3.7450001 -1.96 -3.7450001 -1.96 -3.7450001 -1.96 -3.7450001 -1.96 -3.7450001 -1.96 -3.7450001 -1.96 -3.7450001 -1.96 -3.7800002 -1.96 -3.7800002 -1.96 -3.7800002 -1.995 -3.7800002 -1.995 -3.7800002 -2.03 -3.7800002 -2.0649998 -3.815 -2.135 -3.815 -2.135 -3.815 -2.205 -3.815 -2.24 -3.815 -2.2749999 -3.7800002 -2.3100002 -3.7800002 -2.3100002 -3.7800002 -2.345 -3.7800002 -2.345 -3.7800002 Color red Freehand 65 -4.97 -2.905 -4.935 -2.87 -4.97 -2.87 -4.97 -2.835 -4.97 -2.835 -4.97 -2.835 -4.97 -2.835 -4.97 -2.835 -4.97 -2.8 -4.97 -2.8 -4.935 -2.8 -4.935 -2.8 -4.935 -2.8 -4.9 -2.8 -4.865 -2.8 -4.76 -2.8 -4.725 -2.8 -4.655 -2.8 -4.5499997 -2.8 -4.515 -2.8 -4.48 -2.8 -4.4449997 -2.8 -4.4449997 -2.8 -4.4449997 -2.8 -4.4449997 -2.8 -4.4449997 -2.8 -4.48 -2.765 -4.515 -2.765 -4.5499997 -2.765 -4.585 -2.765 -4.69 -2.765 -4.725 -2.765 -4.83 -2.73 -4.865 -2.73 -4.9 -2.73 -4.935 -2.73 -4.97 -2.73 -4.97 -2.73 -4.97 -2.73 -4.97 -2.73 -4.97 -2.73 -4.97 -2.73 -4.97 -2.73 -4.935 -2.73 -4.935 -2.73 -4.9 -2.73 -4.865 -2.73 -4.83 -2.73 -4.83 -2.73 -4.795 -2.73 -4.76 -2.73 -4.76 -2.73 -4.76 -2.73 -4.76 -2.73 -4.76 -2.73 -4.795 -2.765 -4.83 -2.765 -4.865 -2.8 -4.865 -2.8 -4.865 -2.8 -4.865 -2.8 -4.865 -2.8 -4.865 -2.8 -4.865 -2.8 -4.865 -2.8 Color red Freehand 13 1.12 2.5900002 1.085 2.555 1.085 2.52 1.085 2.415 1.085 2.38 1.085 2.2749999 1.085 2.205 1.085 2.17 1.085 2.1000001 1.085 2.03 1.085 1.995 1.085 1.995 1.085 1.995 Color blue Freehand 35 1.015 2.625 1.0500001 2.695 1.0500001 2.695 1.0500001 2.695 1.0500001 2.695 1.0500001 2.695 1.085 2.73 1.085 2.73 1.12 2.73 1.1550001 2.695 1.19 2.695 1.225 2.695 1.26 2.6599998 1.26 2.6599998 1.2950001 2.625 1.3299999 2.5900002 1.3299999 2.52 1.365 2.415 1.365 2.38 1.365 2.24 1.365 2.17 1.365 2.135 1.3299999 2.03 1.2950001 1.995 1.26 1.96 1.225 1.96 1.1550001 1.9250001 1.12 1.9250001 1.0500001 1.9250001 1.0500001 1.9250001 1.015 1.96 1.015 1.96 1.015 1.96 1.0500001 1.96 1.0500001 1.96 Color blue Freehand 10 1.68 2.555 1.715 2.5900002 1.715 2.5900002 1.715 2.5900002 1.715 2.5900002 1.715 2.5900002 1.715 2.5900002 1.715 2.5900002 1.715 2.5900002 1.715 2.5900002 Color blue Freehand 11 1.715 2.17 1.715 2.0649998 1.715 2.03 1.715 2.03 1.715 1.96 1.715 1.96 1.715 1.9250001 1.715 1.9250001 1.715 1.8900001 1.715 1.8900001 1.715 1.8900001 Color blue Freehand 30 2.1000001 2.6599998 2.135 2.625 2.135 2.5900002 2.17 2.555 2.17 2.52 2.17 2.485 2.17 2.345 2.17 2.2749999 2.17 2.17 2.17 2.1000001 2.17 2.03 2.17 1.96 2.17 1.9250001 2.17 1.8900001 2.17 1.8900001 2.17 1.8549999 2.205 1.8549999 2.205 1.8549999 2.24 1.8549999 2.2749999 1.8549999 2.3100002 1.8549999 2.345 1.8549999 2.38 1.8549999 2.415 1.8549999 2.415 1.8549999 2.45 1.8549999 2.45 1.8199999 2.45 1.8199999 2.45 1.8199999 2.45 1.8199999 Color blue Freehand 14 2.17 2.835 2.17 2.905 2.17 2.905 2.205 2.905 2.205 2.905 2.24 2.905 2.3100002 2.905 2.345 2.905 2.45 2.905 2.485 2.905 2.555 2.905 2.555 2.9399998 2.5900002 2.9399998 2.5900002 2.9399998 Color blue Freehand 12 2.87 2.765 2.87 2.73 2.87 2.6599998 2.87 2.555 2.905 2.485 2.905 2.415 2.905 2.38 2.905 2.2749999 2.9399998 2.24 2.9399998 2.24 2.9399998 2.205 2.9399998 2.205 Color blue Freehand 14 3.1499999 2.2749999 3.1850002 2.24 3.22 2.205 3.22 2.17 3.255 2.135 3.255 2.0649998 3.255 2.03 3.255 1.995 3.255 1.9250001 3.255 1.8199999 3.255 1.8199999 3.255 1.785 3.22 1.785 3.22 1.785 Color blue Freehand 49 3.5 2.695 3.605 2.73 3.6399999 2.73 3.6749997 2.73 3.7099998 2.765 3.7450001 2.8 3.7800002 2.8 3.7800002 2.835 3.815 2.835 3.815 2.835 3.815 2.835 3.7800002 2.835 3.7450001 2.8 3.7450001 2.8 3.7099998 2.8 3.7099998 2.765 3.6749997 2.765 3.6399999 2.73 3.6399999 2.73 3.605 2.695 3.57 2.6599998 3.57 2.6599998 3.5349998 2.625 3.5349998 2.5900002 3.5349998 2.5900002 3.5349998 2.5900002 3.5349998 2.555 3.5349998 2.555 3.5349998 2.52 3.57 2.52 3.57 2.485 3.605 2.485 3.605 2.485 3.6399999 2.485 3.6749997 2.45 3.7099998 2.45 3.7099998 2.45 3.7099998 2.415 3.7099998 2.38 3.7099998 2.345 3.7099998 2.345 3.6749997 2.2749999 3.6749997 2.2749999 3.6399999 2.24 3.6399999 2.24 3.605 2.24 3.57 2.24 3.57 2.24 3.57 2.24 Color blue Freehand 52 3.885 3.08 3.885 3.115 3.8500001 3.115 3.8500001 3.115 3.8500001 3.115 3.885 3.115 3.92 3.1499999 3.955 3.1499999 3.99 3.1499999 4.06 3.1499999 4.1299996 3.1499999 4.165 3.115 4.2000003 3.115 4.2000003 3.08 4.235 3.08 4.235 3.045 4.235 3.01 4.235 2.9399998 4.235 2.87 4.235 2.765 4.235 2.695 4.235 2.5900002 4.235 2.52 4.235 2.45 4.235 2.38 4.235 2.2749999 4.235 2.17 4.235 2.135 4.235 2.0649998 4.27 2.0649998 4.27 2.03 4.27 2.03 4.27 1.995 4.27 1.995 4.27 1.995 4.27 1.995 4.27 1.995 4.27 1.995 4.235 1.995 4.235 1.995 4.2000003 1.995 4.165 1.96 4.1299996 1.96 4.06 1.9250001 4.025 1.9250001 3.955 1.9250001 3.92 1.9250001 3.92 1.9250001 3.885 1.9250001 3.885 1.9250001 3.885 1.9250001 3.885 1.9250001 Color blue Freehand 56 1.085 1.1550001 1.085 1.12 1.085 1.085 1.085 1.015 1.085 0.90999997 1.085 0.73499995 1.085 0.56 1.085 0.45499998 1.085 0.385 1.085 0.28 1.085 0.245 1.085 0.245 1.085 0.245 1.085 0.28 1.085 0.315 1.085 0.42 1.0500001 0.52500004 1.0500001 0.7 1.0500001 0.805 1.085 0.98 1.085 1.0500001 1.12 1.085 1.1550001 1.19 1.225 1.26 1.26 1.2950001 1.2950001 1.3299999 1.3299999 1.3299999 1.365 1.26 1.4 1.225 1.4 1.19 1.4 1.1550001 1.4 1.0500001 1.4 1.015 1.365 0.94500005 1.3299999 0.875 1.3299999 0.875 1.2950001 0.84 1.26 0.84 1.225 0.84 1.225 0.84 1.225 0.84 1.225 0.84 1.26 0.84 1.26 0.84 1.3299999 0.805 1.4 0.73499995 1.435 0.7 1.505 0.595 1.505 0.56 1.54 0.45499998 1.54 0.45499998 1.54 0.42 1.54 0.385 1.54 0.385 1.54 0.385 1.54 0.385 Color blue Freehand 9 1.75 1.19 1.785 1.1550001 1.785 1.1550001 1.785 1.1550001 1.785 1.1550001 1.785 1.1550001 1.785 1.1550001 1.785 1.12 1.785 1.12 Color blue Freehand 11 1.8199999 0.7 1.8549999 0.595 1.8549999 0.56 1.8549999 0.52500004 1.8549999 0.49 1.8549999 0.45499998 1.8549999 0.42 1.8549999 0.42 1.8549999 0.42 1.8549999 0.42 1.8549999 0.42 Color blue Freehand 30 2.24 1.225 2.2749999 1.26 2.2749999 1.26 2.2749999 1.26 2.2749999 1.26 2.2749999 1.26 2.2749999 1.225 2.2749999 1.225 2.2749999 1.1550001 2.2749999 1.12 2.2749999 0.98 2.2749999 0.90999997 2.2749999 0.66499996 2.2749999 0.595 2.2749999 0.49 2.2749999 0.42 2.2749999 0.385 2.2749999 0.35 2.3100002 0.315 2.3100002 0.28 2.345 0.28 2.38 0.245 2.45 0.245 2.485 0.245 2.555 0.21 2.5900002 0.21 2.5900002 0.21 2.625 0.21 2.625 0.21 2.625 0.21 Color blue Freehand 13 2.3100002 1.2950001 2.2749999 1.3299999 2.2749999 1.3299999 2.2749999 1.3299999 2.2749999 1.3299999 2.415 1.26 2.45 1.26 2.52 1.225 2.5900002 1.225 2.625 1.225 2.6599998 1.225 2.695 1.225 2.695 1.225 Color blue Freehand 11 2.625 0.73499995 2.6599998 0.7 2.695 0.73499995 2.73 0.73499995 2.73 0.73499995 2.8 0.73499995 2.835 0.73499995 2.87 0.73499995 2.905 0.73499995 2.905 0.73499995 2.905 0.73499995 Color blue Freehand 42 3.045 1.015 3.08 1.015 3.115 1.0500001 3.115 1.0500001 3.1499999 1.085 3.1499999 1.085 3.1499999 1.085 3.1499999 1.085 3.1499999 1.085 3.1499999 1.085 3.1499999 1.085 3.1499999 1.085 3.115 1.085 3.115 1.085 3.08 1.0500001 3.045 1.015 3.045 0.98 3.01 0.94500005 3.01 0.875 3.01 0.875 3.01 0.84 3.01 0.84 3.01 0.84 3.045 0.84 3.08 0.84 3.08 0.84 3.115 0.875 3.1499999 0.875 3.1499999 0.875 3.1850002 0.875 3.1850002 0.84 3.1850002 0.84 3.1850002 0.805 3.1850002 0.805 3.1850002 0.73499995 3.1499999 0.7 3.115 0.66499996 3.115 0.63 3.045 0.595 3.045 0.56 3.01 0.56 3.01 0.56 Color blue Freehand 7 3.325 0.595 3.36 0.52500004 3.36 0.49 3.36 0.45499998 3.36 0.385 3.36 0.35 3.36 0.35 Color blue Freehand 38 3.43 1.085 3.5 1.12 3.5 1.12 3.5349998 1.12 3.5349998 1.12 3.57 1.1550001 3.605 1.1550001 3.6399999 1.19 3.6749997 1.19 3.6749997 1.1550001 3.7099998 1.12 3.7450001 1.12 3.7450001 1.085 3.7099998 1.015 3.7099998 1.015 3.6749997 0.94500005 3.6399999 0.90999997 3.605 0.875 3.57 0.875 3.57 0.875 3.57 0.875 3.57 0.875 3.57 0.875 3.57 0.875 3.57 0.875 3.605 0.875 3.605 0.875 3.6399999 0.875 3.6749997 0.875 3.7099998 0.84 3.7099998 0.805 3.7099998 0.73499995 3.6749997 0.7 3.6749997 0.66499996 3.6749997 0.63 3.6399999 0.63 3.6399999 0.595 3.6399999 0.595 Color blue Freehand 48 3.7450001 1.4699999 3.7099998 1.505 3.7099998 1.505 3.7099998 1.505 3.7099998 1.505 3.7450001 1.54 3.815 1.54 3.8500001 1.54 3.885 1.505 3.955 1.505 3.99 1.4699999 4.025 1.4699999 4.025 1.435 4.025 1.435 4.025 1.4 4.025 1.3299999 4.025 1.2950001 4.025 1.1550001 4.025 1.12 4.025 1.0500001 4.025 0.98 4.025 0.90999997 4.025 0.805 4.025 0.77 4.025 0.73499995 4.025 0.66499996 4.025 0.63 4.06 0.56 4.06 0.52500004 4.06 0.49 4.06 0.45499998 4.06 0.45499998 4.06 0.42 4.06 0.42 4.06 0.42 4.06 0.42 4.025 0.42 4.025 0.42 3.99 0.385 3.955 0.385 3.92 0.385 3.8500001 0.385 3.815 0.35 3.7800002 0.35 3.7800002 0.315 3.7450001 0.315 3.7450001 0.315 3.7450001 0.315 Color blue

For functions Learn Math Equation: f(^ - 1)^ means "inverse function" NOT Learn Math Equation:(/ 1,/ f)/