Question

select the correct answer from each drop - down menu. the graph of ( g(x) ) is shown. the graph of ( h(x)=g(x + 5) ) has

Explanation:

Step1: Identify horizontal shift rule

For $h(x)=g(x+a)$, if $a>0$, shift left by $a$.

Step2: Apply shift to $g(x)$

Here $a=5$, so shift $g(x)$ left 5 units.

Step3: Find new asymptote and intercept

Original $g(x)$ has horizontal asymptote $y=3$, y-intercept $(0,0)$.
After shift: horizontal asymptote stays $y=3$; new x-intercept: solve $g(x+5)=0$, original $g(0)=0$, so $x+5=0 \implies x=-5$.

Answer:

a horizontal asymptote at $y=3$ and an x-intercept at $x=-5$