Question

Write an equation that represents a vertical translation 7 units down of the graph of g(x)=|x|.

h(x)=

Answer 1

Well, we know what the output of g(x) currently. The y-intercept is located at the origin and is in the shape of a v opening upwards with the slopes of 1 and -1. In order to perform a translation, we can either change the output of x with |x-a| or |x| - b, where a and b are any constant. When you graph two examples of those translations, you can find out which is a vertical translation and which is a horizontal translation. The last thing you need is to just plug in 7 as your constant, as it has to be translated by 7 units. Thus, you find your h(x).

Answer 2

Horizontal translations are in the form of |x-a|, while vertical translations are in the form of |x| - b. The reason why this is the case is because if you plug in any value for x and a, you will ALWAYS get a NONNEGATIVE value. Thus, this cannot ever fall beneath the x axis. However, with |x| - b, as long as x < b, the function will always be below the x axis. Thus, your h(x) = |x| - 7.