which exponential function is represented by the graph?\n○ f(x)=2(3^x)\n○ f(x)=3(3^x)\n○ f(x)=3(2^x)\n○…

Explanation:

Step1: Recall the general form of exponential function

The general form of an exponential function is $f(x)=a(b^{x})$, where $a$ is the y - intercept (value of the function when $x = 0$) and $b$ is the base.

Step2: Find the y - intercept

From the graph, when $x = 0$, $y=f(0)=2$. Substituting $x = 0$ into $f(x)=a(b^{x})$, we get $f(0)=a(b^{0})=a$. So $a = 2$.

Step3: Use another point to find the base

We know the point $(1,4)$ lies on the graph. Substitute $a = 2$, $x = 1$ and $y=4$ into $f(x)=a(b^{x})$. So $4=2(b^{1})$. Solving for $b$ gives $b = 2$.

Answer:

$f(x)=2(2^{x})$