Question

graph the function $f(x) = 2(2)^{x + 8}$ on the axes below. you must plot the asymptote and any two points with integer coordinates. asymptote: axes with y and x axes, some plotted points

Explanation:

Step1: Find the asymptote

For exponential functions $f(x)=a(b)^{x+c}$, the horizontal asymptote is $y=0$.

Step2: Calculate first integer point

Let $x=-8$: $f(-8)=2(2)^{-8+8}=2(2)^0=2(1)=2$. Point: $(-8,2)$.

Step3: Calculate second integer point

Let $x=-7$: $f(-7)=2(2)^{-7+8}=2(2)^1=4$. Point: $(-7,4)$.

Answer:

Asymptote: $y=0$
Points: $(-8,2)$, $(-7,4)$
(Plot the horizontal line $y=0$, then mark the two points on the graph.)