# Transforming the Absolute Value Function

You will see two functions graphed. The first is a fixed function, $f(x) = |x|$. The second function, g(x) is able to be changed. I have defined $g(x) = A*|Bx + C| + D$, where A, B, C and D are all coefficients that affect the graph of g(x) differently. By default, A and B = 1 while C and D = 0, so $g(x) = |x|$. You may move the sliders to change the values of these coefficients and compare the blue-dashed line representing g(x) to the black-solid line that represents f(x).

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Respond to the following questions on the labsheet that was passed out.

1) What changes does moving slider A have on the graph?

2) What changes does moving slider B have on the graph?

3) What changes does moving slider C have on the graph?

4) What changes does moving slider D have on the graph?

5) How are the effects of changing A and B similar? different? Why does this occur?

6) How does changing the shape and position of the absolute value function compare to changing the slope and y-intercept of a linear function?

7) Under free objects, you will see two open circles next to the linear functions h(x) and i(x). Click on those circles to display two lines. Notice that these lines intersect and continue to form the function f(x). Move the sliders so that $g(x) = |0.5x - 3| - 2$. What two lines intersect to form g(x)? You may double click the objects h(x) and i(x) to redefine them and test your solution.

8) How do the slope and y-intercept of these two lines compare to the coefficients of g(x)?

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