Question

1. the functions $f(x)$ and $g(x)$ are shown on the graph to the right. if $g(x) = f(x - h)$, what is the value of $h$?

Explanation:

Step1: Identify a point on $g(x)$

Take the y-intercept of $g(x)$: $(0, 2)$

Step2: Find matching point on $f(x)$

Find the point on $f(x)$ with $y=2$: $(-3, 2)$

Step3: Apply horizontal shift rule

For $g(x)=f(x-h)$, substitute $x=0$, $f(x-h)=f(-3)$:
$0 - h = -3$

Step4: Solve for $h$

$h = 0 - (-3) = 3$

Answer:

$3$