Question

Which function represents the graph of h(x)=2|x−3|+1 after it is translated 2 units to the right? f(x)=2|x−3|−1f(x)=2|x−3|+3f(x)=2|x−5|+1f(x)=2|x−1|+1

Answer 1

Given the function;

`h(x)=2|x-3|+1`

A translation is a slide, which means that the function has the same shape graphically, but the graph of the function slides up or down or slides left or right to a different position on the coordinate plane.

Thus, when a function h(x) is translated c-units to the right, it becomes h(x-c).

Thus, the given function is translated 2 units to the right. We have;

`\begin{gathered} h(x-2)=f(x)=2|x-2-3|+1 \\ f(x)=2|x-5|+1 \end{gathered}`