Question

choose the graph of the function.
$f(x) = 2 \cdot 3^x$
choose 1 answer:
a
graph a
b
graph b
c
graph c

Explanation:

Step1: Find y-intercept (x=0)

$f(0)=2\cdot3^0=2\cdot1=2$

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

$f(1)=2\cdot3^1=2\cdot3=6$

Step3: Test negative x-value (x=-1)

$f(-1)=2\cdot3^{-1}=2\cdot\frac{1}{3}=\frac{2}{3}\approx0.67$

Step4: Match to graph

Check which graph passes through (0,2), (1,6), and approaches 0 as $x\to-\infty$.

Answer:

A. <The graph passing through (0,2), rising steeply for positive x, and approaching 0 for negative x>