Find g(x), where g(x) is the translation 10 units down of f(x)=|x|. Write your answer in the form a|x–h|+k, where a, h, and k are integers.

Answer 1

In the form f(x) = a|x-h| + k, the "a" causes a vertical stretch, the "h" a horizontal shift, and the "k" a vertical shift. Since the problem only suggests a vertical shift (down), k = -10, a=1 (no vertical stretch or shrink), h = 0 (no horizontal shift).

So, g(x) = |x| - 10

Here is a Desmos graph you can use to confirm (and use sliders to adjust values for a,h, to see the different transformations to f(x).

desmos.com/calculator/x4qmm3c10a