Fill in the blanks. Transformations of Graphs Symbolic Representation T justific

Question

Fill in the blanks. Transformations of Graphs Symbolic Representation T justification of the connection between the Verbal Representation Representation (of the geometri transformations) the transformed function) geometric and function transformations y h(x) 3 Shift up 3 Reflection over the y-axis Shifted upward 3 units Slide 3 units up, then reflection y (h(x) 3) over the x-axis The function reflects about the y- axis (x, y) (-x, y) (-x 3, y) h(-(x-3) Reflection over the y-axis, then y x, h(x)) (-x, h(x)) (-x 3, h(x)) or equivalently Let x' x 3. Then x (x-3) slide 3 units to the right So the transformed point is (x',h(-(x 3)) Shift left 3, then y (x +3) 3 shift up 3 october 2010

Explanation / Answer

1. y = h(x) + 3

parent function h(x) when shifted 3 units upwards it becomes h(x) + 3

2. y = h(-x) + 3

parent function h(x) is reflected over y axis it becomes h(-x) and then shifted 3 units upwards

h(-x) + 3

3. y = -h(x) + 3

parent function h(x) is reflected over x axis it becomes h(-x) and then shifted 3 units upwards

- h (x) + 3

4. y = h (-x)

parent function h(x) is reflected over y axis

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