Question

The solid line is the parent function, f(x). Which of the following dotted line graphs shows the translation of f(x) = f(x + 0.5)

Answer 1

Given

The graph of the parent function f(x) is,

To find:

The graph representing the translation f(x+0.5) of f(x).

Explanation:

It is given that,

The graph of the parent function f(x) is,

That implies,

The equation of f(x) is,

$\begin{gathered} x+\frac{y}{-2}=1 \\ x-1=\frac{y}{2} \\ y=2(x-1) \\ f(x)=2x-2 \end{gathered}$

Then,

$\begin{gathered} f(x+0.5)=2(x+0.5)-2 \\ =2x+1-2 \\ f(x+0.5)=2x-1 \end{gathered}$

Therefore, the graph of the translation f(x+0.5) is,