Period: __ Number: Date: _______ Name: _________________

MATH PROJECT: TRANSFORMING FUNCTIONS (Due: Monday, December 05, 2016)Given: Monday, October 03, 2016 Use the following website to graph:www.graphsketch.com Use the following website to graph Absolute Value Functions: https://www.demos.com/calculatorYou can use the other tools to graph, if possible.) RUBRIC: (Part A: 20 points; Part B: 20 points; Part C: 20 points; Part D: 20 points; Part E: 20 points)You can use other tools to graph, if possible.Basic Functions:

A. LINEAR FUNCTION: f(x) = xB. QUADRATIC FUNCTION (PARABOLA): f(x) = x2

C. EXPONENTIAL GROWTH FUNCTION: f(x) = 2x D. EXPONENTIAL DECAY FUNCTION: f(x) = 0.25x E. ABSOLUTE VALUE FUNCTION f(x) = |x|

Let g(x) be the image f(x). For #11 and 12: Label the image functions: g(x), h(x), i(x), j(x),…1. Reflect over the x-axis 2. Reflect over the y-axis 3. Horizontal translation to the left 3 units 4. Horizontal translation to the right 3 units 5. Vertical translation up 3 units 6. Vertical translation down 3 units 7. Horizontal stretch by the scale factor of 4 8. Horizontal compression by the scale factor of 0.25 9. Vertical stretch by the scale factor of 5 10. Vertical compression by the scale factor of 0.2 11. Vertical stretch by the scale factor of 5, translation to the left 3 units, then reflect over

the x-axis.12. Vertical compression by the scale factor of 0.2, then vertical translation down 3 units.

INSTRUCTIONS:1) Fill out the packet with the ranges and domains. (Do this after you graph, so you can see

the domain and the range easily.)2) Go to https://www.desmos.com/calculator3) Write and graph your functions.

4) If you are on a Mac: hold command + shift + 3 and drag over the graphIf you are on a Windows computer: Go to the snipping tool application and click on “New Snip”, drag over the graph, and click the purple save logo to save the capture.

5) Go to word6) Go to insert pictures and find your capture7) Go to format text wrapping in front of text8) Use the green circle to turn 90 degrees9) Drag it to the center of the top of the page10) Do the same for other graphs, and put it on the bottom of the same page.

PART A: LINEAR FUNCTION: f(x) = x

1. Reflect over the x-axis Domain             Range

f(x) = x (-∞, +∞)         (-∞, +∞)            g(x) = -x (-∞, +∞)         (-∞, +∞)            Graph f(x) and g(x) on the same coordinate grid.

2. Reflect over the y-axis Domain             Range

f(x) = x (-∞, +∞)         (-∞, +∞)            g(x) = (-x) = -x (-∞, +∞)         (-∞, +∞)            Graph f(x) and g(x) on the same coordinate grid.

3. Horizontal translation to the left 3 units Domain             Range

f(x) = x (-∞, +∞)          (-∞, +∞)            g(x) = (x+3) (-∞, +∞)          (-∞, +∞)            Graph f(x) and g(x) on the same coordinate grid.

4. Horizontal translation to the right 3 units

Domain             Range f(x) = x (-∞, +∞)         (-∞, +∞)            g(x) = (x-3) (-∞, +∞)         (-∞, +∞)            Graph f(x) and g(x) on the same coordinate grid.

5. Vertical translation up 3 unitsDomain             Range

f(x) = x (-∞, +∞)          (-∞, +∞)            g(x) = x + 3 (-∞, +∞)          (-∞, +∞)            Graph f(x) and g(x) on the same coordinate grid.

6. Vertical translation down 3 units Domain             Range

f(x) = x (-∞, +∞)          (-∞, +∞)             g(x) = x - 3 (-∞, +∞)          (-∞, +∞)            Graph f(x) and g(x) on the same coordinate grid.

7. Horizontal stretch by the scale factor of 4.(Multiply x by the reciprocal of given SF)(0.25)

Domain             Range f(x) = x (-∞, +∞)          (-∞, +∞)            g(x) = 0.25x (-∞, +∞)          (-∞, +∞)            Graph f(x) and g(x) on the same coordinate grid.

PART A (Cont.)8. Horizontal compression by the scale factor of 0.25

(Multiply x by the reciprocal of given SF)(4)

Domain             Range f(x) = x (-∞, +∞)          (-∞, +∞)            g(x) = 4x (-∞, +∞)          (-∞, +∞)            Graph f(x) and g(x) on the same coordinate grid.

9. Vertical stretch by the scale factor of 5 Domain             Range

f(x) = x (-∞, +∞)          (-∞, +∞)            g(x) = 5x (-∞, +∞)          (-∞, +∞)            Graph f(x) and g(x) on the same coordinate grid.

10. Vertical compression by the scale factor of 0.2 Domain             Range

f(x) = x (-∞, +∞)             (-∞, +∞)            g(x) = 0.2x (-∞, +∞)             (-∞, +∞)            Graph f(x) and g(x) on the same coordinate grid.

Domain             Range f(x) = x (-∞, +∞)             (-∞, +∞)            g(x) = 0.2x (-∞, +∞)             (-∞, +∞)            Graph f(x) and g(x) on the same coordinate grid.

11. Vertical stretch by the scale factor of 5, translation to the left 3 units, then reflects over the x-axis.

Domain             Range f(x) = x (-∞, +∞)   (-∞, +∞)            g(x) = 5x (Vertical Stretch, SF: 5)

(-∞, +∞)   (-∞, +∞)            h(x) = 5(x+3) (Left 3) (-∞, +∞)   (-∞, +∞)            i(x) = -5(x+3) (Final Function)(-∞, +∞)(-∞, +∞)          Graph f(x), g(x), h(x), i(x) on the same coordinate grid.

12. Vertical compression by the scale factor of 0.2, then vertical translation down 3 units.

Domain             Range f(x) = x (-∞, +∞)             (-∞,+∞)            g(x) = 0.2x (-∞, +∞)             (-∞, +∞)            h(x) = 0.2x-3 (-∞, +∞)             (-∞, +∞)          Graph f(x), g(x), h(x) on the same coordinate grid.

PART B: QUADRATIC FUNCTION: f(x) = x2

1. Reflect over the x-axis. Domain             Range

f(x) = x2 (-∞, +∞)            [0, +∞) g(x) = -f(x) = - x2 (-∞, +∞)           (-∞, 0] Graph f(x) and g(x) on the same coordinate grid.

2. Reflect over the y-axis. Domain             Range

f(x) = x2 (-∞, +∞)            [0, +∞) g(x) = f(-x) = (-x)2 ) = x2 (-∞, +∞)            [0,+∞) Graph f(x) and g(x) on the same coordinate grid.

3. Horizontal translation to the left 3 units. Domain             Range

f(x) = x2 (-∞, +∞)            [0, +∞) g(x) = f(x+3) = (x + 3)2 (-∞, +∞)            [0,+∞) Graph f(x) and g(x) on the same coordinate grid.

4. Horizontal translation to the right 3 units Domain             Range

f(x) = x2 (-∞, +∞)            [0, +∞) g(x) = f(x-3) = (x - 3)2 (-∞, +∞)            [0,+∞) Graph f(x) and g(x) on the same coordinate grid.

5.Vertical translation up 3 unitsDomain             Range

f(x) = x2 (-∞, +∞)            [0, +∞) g(x) = f(x) + 3 = x2 + 3 (-∞, +∞)            [3,+∞) Graph f(x) and g(x) on the same coordinate grid.

6.Vertical translation down 3 units Domain             Range

f(x) = x2 (-∞, +∞)            [0, +∞) g(x) = f(x) - 3= x2 - 3 = x2 - 3

(-∞, +∞)            [-3,+∞) Graph f(x) and g(x) on the same coordinate grid.

7.Horizontal stretch by the scale factor of 4.(Multiply x by the reciprocal of 4: 0.25)

Domain             Range f(x) = x2 (-∞, +∞)            [0, +∞) g(x) = f(0.25x) = 0.25x2 (-∞, +∞)            [0,+∞) Graph f(x) and g(x) on the same coordinate grid.

8.Horizontal compression by the scale factor of 0.25. (Multiply x by the reciprocal of 0.25 which is 4)

Domain             Range f(x) = x2 (-∞, +∞)            [0, +∞) g(x) = f(4x) = 4x2 (-∞, +∞)            [0,+∞) Graph f(x) and g(x) on the same coordinate grid.

9.Vertical stretch by the scale factor of 5. Domain             Range

f(x) = x2 (-∞, +∞)            [0, +∞) g(x) = 5.f(x)= 5x2 (-∞, +∞)            [0,+∞) Graph f(x) and g(x) on the same coordinate grid.

10. Vertical compression by the scale factor of 0.2

Domain             Range f(x) = x2 (-∞, +∞)            [0, +∞) g(x) = (0.2).f(x)= 0.2x2 (-∞, +∞)            [0,+∞)Graph f(x) and g(x) on the same coordinate grid.

11. Vertical stretch by the scale factor of 5, translation to the left 3 units, then reflects over the x-axis.

Domain             Range f(x) = x2 (-∞, +∞)            [0, +∞) g(x) = 5.f(x)= 5x2 (-∞, +∞)            [0,+∞)h(x) = 5.f(x+3) = 5(x+3)2

(-∞, +∞)            [0,+∞)i(x) = -5.f(x+3) = -5(x+3)2

(-∞, +∞)            (-∞,0]Graph f(x), g(x), h(x), i(x) on the same coordinate grid.

12. Vertical compression by the scale factor of 0.2, then vertical translation down 3 units.

Domain             Range f(x) = x2 (-∞, +∞)            [0, +∞) g(x) = (0.2).f(x)= 0.2x2 (-∞, +∞)            [0,+∞)h(x) = 0.2.f(x) - 3= 0.2x2 -3

(-∞, +∞)            [-3, +∞)

Graph f(x), g(x), h(x) on the same coordinate grid.PART C: EXPONENTIALGROWTH FUNCTION: f(x) = 2x

1.Reflect over the x-axis Domain             Range

f(x) = 2x (-∞, +∞)            (0,+∞)g(x) = -2x (-∞, +∞)            (-∞, 0)Graph f(x) and g(x) on the same coordinate grid.

2.Reflect over the y-axis

Domain             Range f(x) = 2x (-∞, +∞)            (0,+∞)g(x) = 2-x (-∞, +∞)            (0, +∞)Graph f(x) and g(x) on the same coordinate grid.

3.Horizontal translation to the left 3 units

Domain             Range f(x) = 2x (-∞, +∞)            (0,+∞)g(x) = 2(x+3) (-∞, +∞)            (0,+∞)Graph f(x) and g(x) on the same coordinate grid.

4.Horizontal translation to the right 3 units Domain             Range

f(x) = 2x (-∞, +∞)            (0,+∞) g(x) = 2(x-3) (-∞, +∞)            (0,+∞)Graph f(x) and g(x) on the same coordinate grid.

5.Vertical translation up 3 unitsDomain             Range

f(x) = 2x (-∞, +∞)            (0,+∞)g(x) = 2x+3 (-∞, +∞)            (3,+∞)Graph f(x) and g(x) on the same coordinate grid.

6.Vertical translation down 3 units Domain             Range

f(x) = 2x (-∞, +∞)            (0,+∞)g(x) = 2x-3 (-∞, +∞)            (-3,+∞)

Graph f(x) and g(x) on the same coordinate grid.

7.Horizontal stretch by the scale factor of 4. (Multiply x by the reciprocal of 4 which is 0.25)

Domain             Range f(x) = 2x (-∞, +∞)            (0,+∞)g(x) = 2(0.25x) (-∞, +∞)            (0,+∞)Graph f(x) and g(x) on the same coordinate grid.PART C (Cont.)

8.Horizontal compression by the scale factor of 0.25 (Multiply x by the reciprocal of 0.25 which is 4)

Domain             Range f(x) = 2x (-∞, +∞)            (0, +∞)g(x) = 2(4x) (-∞, +∞)            (0, +∞)Graph f(x) and g(x) on the same coordinate grid.

9.Vertical stretch by the scale factor of 5. Domain             Range

f(x) = 2x (-∞, +∞)            (0,+∞)g(x) = (5). 2x (-∞, +∞)            (0, +∞)Graph f(x) and g(x) on the same coordinate grid.

10. Vertical compression by the scale factor of 0.2.

Domain             Range f(x) = 2x (-∞, +∞)            (0,+∞)g(x) = (0.2). 2x (-∞, +∞)            (0, +∞)Graph f(x) and g(x) on the same coordinate grid.

11. Vertical stretch by the scale factor of 5, translation to the left 3 units, then reflects over the x-axis.

Domain           Range f(x) = 2x (-∞, +∞)          (0,+∞)g(x) = (5). 2x (Vertical Stretch, SF: 5)

(-∞, +∞)          (0, +∞)h(x) = (5). 2(x+3) (Left 3) (-∞, +∞)          (0, +∞)i(x) = -(5). 2(x+3) (Final Function)

(-∞, +∞)          (-∞, 0)Graph f(x), g(x), h(x), i(x) on the same coordinate grid.

12. Vertical compression by the scale factor of 0.2, then vertical translation down 3 units.

Domain             Range f(x) = 2x (-∞, +∞)            (0,+∞)

g(x) = (0.2). 2x (-∞, +∞)          (0, +∞)h(x) = (0.2). 2x -3 (-∞, +∞)          (-3, +∞)

Graph f(x), g(x), h(x) on the same coordinate grid.

PART D: EXPONENTIAL DECAY FUNCTION: f(x) = f(x) = 0.5x

1.Reflect over the x-axis Domain             Range

f(x) = 0.5x (-∞, +∞)            (0,+∞)g(x) = -0.5x (-∞, +∞)            (-∞, 0)Graph f(x) and g(x) on the same coordinate grid.

2.Reflect over the y-axis Domain             Range

f(x) = 0.5x (-∞, +∞)            (0,+∞)g(x) = 0.5-x (-∞, +∞)            (0,+∞)Graph f(x) and g(x) on the same coordinate grid.

3.Horizontal translation to the left 3 units Domain             Range

f(x) = 0.5x (-∞, +∞)            (0,+∞)g(x) = 0.5(x+3) (-∞, +∞)            (0,+∞)Graph f(x) and g(x) on the same coordinate grid.

4.Horizontal translation to the right 3 units Domain             Range

f(x) = 0.5x (-∞, +∞)            (0,+∞)g(x) = 0.5(x-3) (-∞, +∞)            (0,+∞)Graph f(x) and g(x) on the same coordinate grid.

5.Vertical translation up 3 unitsDomain             Range

f(x) = 0.5x (-∞, +∞)            (0,+∞)g(x) = 0.5x +3 (-∞, +∞)            (3, +∞)Graph f(x) and g(x) on the same coordinate grid.

6.Vertical translation down 3 units Domain             Range

f(x) = 0.5x (-∞, +∞)            (0,+∞)g(x) = 0.5x -3 (-∞, +∞)           (-3, +∞)Graph f(x) and g(x) on the same coordinate grid.

7.Horizontal stretch by the scale factor of 4. (Multiply x by the reciprocal of 4)

Domain             Range f(x) = 0.5x (-∞, +∞)            (0,+∞)g(x) = 0.50.25x (-∞, +∞)            (0,+∞)Graph f(x) and g(x) on the same coordinate grid.PART D (Cont.)

8.Horizontal compression by the scale factor of 0.25. (Multiply x by the reciprocal of 0.25)

Domain             Range f(x) = 0.54x (-∞, +∞)            (0,+∞)g(x) = (-∞, +∞)            (0,+∞)Graph f(x) and g(x) on the same coordinate grid.

9.Vertical stretch by the scale factor of 5 Domain             Range

f(x) = 0.5x (-∞, +∞)            (0,+∞)g(x) = 5.(0.5)x (-∞, +∞)            (0,+∞)Graph f(x) and g(x) on the same coordinate grid.

10. Vertical compression by the scale factor of 0.2

Domain             Range f(x) = 0.5x (-∞, +∞)            (0,+∞)g(x) = (0.2).(0.5)x (-∞, +∞)            (0,+∞)Graph f(x) and g(x) on the same coordinate grid.

11. Vertical stretch by the scale factor of 5, translation to the left 3 units, then reflects over the x-axis.

Domain    Range

f(x) = 0.5x (-∞, +∞)     (0,+∞)g(x) = (5).0.5x (Vertical Stretch, SF: 5)

(-∞, +∞)     (0,+∞)h(x) = (5).0.5(x+3) (Left 3)

(-∞, +∞)     (0,+∞)i(x) = -(5).0.5x (Final Function)

(-∞, +∞)     (-∞, 0)Graph f(x), g(x), h(x), i(x) on the same coordinate grid.

12. Vertical compression by the scale factor of 0.2, then vertical translation down 3 units.

Domain        Range f(x) = 0.5x (-∞, +∞)       (0,+∞)g(x) = (0.2).0.5x (-∞, +∞)       (0,+∞)h(x) = (0.2).0.5x -3 (-∞, +∞)       (-3,+∞)Graph f(x), g(x), h(x) on the same coordinate

grid.

PART E: ABSOLUTE VALUE FUNCTION: f(x) = |x|

1.Reflect over the x-axis Domain          Range

f(x) = |x| (-∞, +∞)         [0, +∞)

g(x) = -|x| (-∞, +∞)         (-∞, 0]            Graph f(x) and g(x) on the same coordinate grid.

2.Reflect over the y-axis Domain           Range

f(x) = |x| (-∞, +∞)          [0, +∞)g(x) = |-x| (-∞, +∞)          [0, +∞)Graph f(x) and g(x) on the same coordinate grid.

3.Horizontal translation to the left 3 units Domain             Range

f(x) = |x| (-∞, +∞)            [0, +∞)g(x) = |x+3| (-∞, +∞)            [0, +∞)Graph f(x) and g(x) on the same coordinate grid.

4.Horizontal translation to the right 3 units Domain             Range

f(x) = |x| (-∞, +∞)            [0, +∞)g(x) = |x-3| (-∞, +∞)            [0, +∞)Graph f(x) and g(x) on the same coordinate grid.

5.Vertical translation up 3 unitsDomain             Range

f(x) = |x| (-∞, +∞)            [0, +∞)

g(x) = |x|+3 (-∞, +∞)      [3, +∞)Graph f(x) and g(x) on the same coordinate grid.

6.Vertical translation down 3 units Domain             Range

f(x) = |x| (-∞, +∞)            [0, +∞)g(x) = |x|-3 (-∞, +∞)            [-3, +∞)Graph f(x) and g(x) on the same coordinate grid.

7.Horizontal stretch by the scale factor of 4.

(Multiply x by the reciprocal of 4)

Domain             Range f(x) = |x| (-∞, +∞)            [0, +∞)g(x) = |0.25x| (-∞, +∞)            [0, +∞)Graph f(x) and g(x) on the same coordinate grid.

8.Horizontal compression by the scale factor of 0.25. (Multiply x by the reciprocal of 0.25)

Domain             Range f(x) = |x| (-∞, +∞)            [0, +∞)g(x) = |4x| (-∞, +∞)            [0, +∞)Graph f(x) and g(x) on the same coordinate grid.

9.Vertical stretch by the scale factor of 5

Domain             Range f(x) = |x| (-∞, +∞)            [0, +∞)g(x) = 5|x| (-∞, +∞)            [0, +∞)Graph f(x) and g(x) on the same coordinate grid.

10. Vertical compression by the scale factor of 0.2

Domain             Range f(x) = |x| (-∞, +∞)            [0, +∞)g(x) = 0.2|x| (-∞, +∞)            [0, +∞)Graph f(x) and g(x) on the same coordinate grid.

11. Vertical stretch by the scale factor of 5, translation to the left 3 units, then reflects over the x-axis.

Domain       Range f(x) = |x| (-∞, +∞)      [0, +∞)

g(x) = 5|x| (Vertical Stretch, SF: 5)(-∞, +∞)             [0, +∞)

h(x) = 5|x+3| (Left 3)

(-∞, +∞)             [0, +∞)i(x) = -5|x+3| (Final Function)

(-∞, +∞)             (-∞, 0]Graph f(x), g(x), h(x), i(x) on the same coordinate grid.

12. Vertical compression by the scale factor of 0.2, then vertical translation down 3 units.

Domain       Range f(x) = |x| (-∞, +∞)             [0, +∞)g(x) = 0.2|x| (-∞, +∞)             [0, +∞)h(x) = 0.2|x| -3 (-∞, +∞)             [-3, +∞)Graph f(x), g(x), h(x) on the same coordinate

grid.