Question

choose the graph of the function.
$g(x) = 2 \cdot 4^x$
choose 1 answer:
a
graph a
b
graph b
c
graph c

Explanation:

Step1: Find y-intercept (x=0)

Substitute $x=0$ into $g(x)$:
$g(0)=2\cdot4^0=2\cdot1=2$
So the graph passes through $(0, 2)$.

Step2: Test another x-value (x=1)

Substitute $x=1$ into $g(x)$:
$g(1)=2\cdot4^1=2\cdot4=8$
So the graph passes through $(1, 8)$.

Step3: Match points to graphs

Check which graph goes through $(0,2)$ and $(1,8)$. Graph A passes through these points, while Graph B passes through $(0,0)$ and Graph C has a higher y-intercept.

Answer:

A. <The graph passing through (0, 2) and (1, 8), with exponential growth approaching 0 as x approaches negative infinity>