Question

The speedometer in Henry's car is broken. The function y = |x - 8| represents the difference y between the car's actual speed x and the displayed speed. a) Describe the translation. Then graph the function.

Answer 1

In general, given a function f(x), a horizontal translation by b units is expressed by the transformation below

`\begin{gathered} f(x)\rightarrow f(x-b) \\ b>0\rightarrow\text{ b units to the right} \\ b<0\rightarrow\text{ b units to the left} \end{gathered}`

Then, in our case, y is a translation of |x| 8 units to the right.

The graph of the function is