Question

rtical stretches and shrinks of exponential functions which exponential function is represented by the graph? $f(x)=2(2^x)$ $f(x)=3(3^x)$ $f(x)=3(2^x)$ $f(x)=2(3^x)$

Explanation:

Step1: Recall exponential form

The general form of an exponential function is $f(x)=a(b^x)$, where $a$ is the y-intercept, and $b$ is the base.

Step2: Identify y-intercept from graph

The graph passes through $(0,3)$. Substitute $x=0$, $f(0)=3$:
$3=a(b^0) \implies 3=a(1) \implies a=3$

Step3: Use point (1,6) to find b

Substitute $a=3$, $x=1$, $f(1)=6$:
$6=3(b^1) \implies b=\frac{6}{3}=2$

Step4: Verify with (-1,1.5)

Substitute $x=-1$, $a=3$, $b=2$:
$f(-1)=3(2^{-1})=3\times\frac{1}{2}=1.5$, which matches the point.

Answer:

$f(x)=3(2^x)$