## Transformations of Functions Worksheet

Open the following webpage:
http://www.langara.bc.ca/mathstats/resource/GraphExplorer/v111/ShiftAndScale.html.

Type in a quadratic function: e.g., for the function y = 3x^{2} – 5x + 2,
type in 3*x^2–5*x+2. Hit ENTER.
If the function does not appear on the graph, then click on the ZoomOut button until it appears.

For each section, when you make a selection, the function will appear to change color. At the bottom right of the
page, there is a slider for c. Move the slider to check what happens to the
function for different values of c.
There will be two graphs: the original function [i.e., f(x)]
and the new function [e.g., f(x+c)]. You will need to answer the following questions:

- Does the function shift? If so, how and for what values of c?
- Does the function reflect over one of the axes? If so, which axes and for what values of c?
- Does the function shrink or stretch? If so, which one, in which direction and for what values of c?

1. Select the f(x+c) box. Move
the slider to check what happens to the function for the following values of c
and answer the questions above:

- c > 1
- 0 < c < 1
- –1 < c < 0
- c < –1
- c = 1
- c = –1

2. Deselect the f(x+c) box.
Select the f(x)+c box. Move
the slider to check what happens to the function for the same values of c and answer
the questions above.

3. Deselect the f(x)+c box.
Select the f(cx) box.
Move the slider to check what happens to the function for
the same values of c and answer the questions above (NOTE: To expand the values of
c, click on the < > button).

4. Deselect the f(cx) box.
Select the cf(x) box.
Move the slider to check what happens to the function for the
same values of c and answer the questions above.

Submit your answers to the four questions with at least two screenshots for each of the questions.

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