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

Answer:

C. $f(x)=3(2^{x})$

Explanation:

Step1: Recall exponential - function form

The general form of an exponential function is $y = ab^{x}$, where $a$ is the $y$ - intercept and $b$ is the base.

Step2: Determine the y - intercept

The graph intersects the $y$ - axis at the point $(0,3)$. Substituting $x = 0$ into $y=ab^{x}$, we get $y=a\times b^{0}=a$. So, $a = 3$.

Step3: Use another point to find the base

We know the point $(1,6)$ lies on the graph. Substitute $a = 3$, $x = 1$, and $y = 6$ into $y=ab^{x}$. We have $6=3\times b^{1}$. Solving for $b$ gives $b = 2$. So the function is $f(x)=3(2^{x})$.