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 = 3x² – 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:

1. Does the function shift? If so, how and for what values of c?
2. Does the function reflect over one of the axes? If so, which axes and for what values of c?
3. 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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