Library+of+Functions-Target+B-Graphing+Abs-Quick+Check+Solutions

1) Compare the graph of the function j(x) = -|x + 4| + 8 to the graph of the reference function.

a: -1; graph opens down h: adding a 4 so the graph is translated left k: adding an 8 so the graph is translated up

The graph of j(x) opens down, and is translated left and up in comparison to the graph of f(x) = |x|.

2) Write an absolute value function that has the following characteristics: opens up, compressed, and is translated to the left and down.

There is an infinite amount of possibilities for this function, but in order for the graph of the function to have the characteristics listed in the problem, the a, h, and k, would have to be as follows:

a: would need to be postiive in order to open up, and would need to fall between 0 and 1 (0 < |a| < 1) in order to be compressed h: would need to add an h value for the graph to translate left k: would need to subtract a k value for the graph to translate down

So one possible answer: g(x) = 1/4 |x + 1| - 6

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