which function represents exponential growth?\n$f(x)=3x$\n$f(x)=x^{3}$\n$f(x)=x + 3$\n$f(x)=3^{x}$

Answer:

D. $f(x)=3^{x}$

Explanation:

Step1: Recall function forms

Linear function: $f(x)=ax + b$ (e.g., $f(x)=x + 3$ where $a = 1,b=3$). Power - function: $f(x)=x^{n}$ (e.g., $f(x)=x^{3}$ where $n = 3$). Proportional function: $f(x)=ax$ (e.g., $f(x)=3x$ where $a = 3$). Exponential function: $f(x)=a^{x}$ ($a>1$ for growth), here $f(x)=3^{x}$ with $a = 3>1$.

Step2: Identify growth type

The function $f(x)=3^{x}$ is an exponential function with base $a = 3>1$, so it represents exponential growth.