which function is a shrink of the exponential growth function shown on the graph?\n○ (f(x)=2(3)^{x})\n○…

Explanation:

Step1: Recall exponential - function transformation rules

For an exponential function of the form $y = a\cdot b^{x}$, if $|a| < 1$, it is a vertical shrink of the exponential function $y = b^{x}$. An exponential growth function has $b>1$.

Step2: Analyze each option

• Option 1: $f(x)=2(3)^{x}$, here $a = 2>1$, it is a vertical stretch.
• Option 2: $f(x)=\frac{1}{2}(3)^{x}$, here $a=\frac{1}{2}<1$ and $b = 3>1$, it is a vertical shrink of the exponential growth function $y = 3^{x}$.
• Option 3: $f(x)=2(\frac{1}{3})^{x}$, here $b=\frac{1}{3}<1$, it is an exponential decay function.
• Option 4: $f(x)=\frac{1}{2}(\frac{1}{3})^{x}$, here $b=\frac{1}{3}<1$, it is an exponential decay function.

Answer:

$f(x)=\frac{1}{2}(3)^{x}$