which graph represents an exponential function?

Explanation:

Step1: Recall exponential - function properties

An exponential function of the form $y = a\cdot b^{x}$ ($a\neq0$, $b>0,b\neq1$) has a horizontal asymptote. When $a>0$ and $b > 1$, the function is an increasing function with a horizontal asymptote at $y = 0$ (the $x$ - axis), and when $a>0$ and $0 < b<1$, the function is a decreasing function with a horizontal asymptote at $y = 0$.

Step2: Analyze the graphs

• The first graph has a horizontal asymptote and is a decreasing function for $x\in R$, which can be of the form $y=a\cdot b^{x}$ where $a>0$ and $0 < b<1$.
• The second graph has a horizontal asymptote and is an increasing function for $x\in R$, which can be of the form $y=a\cdot b^{x}$ where $a>0$ and $b > 1$.
• The third graph does not have a horizontal asymptote and is not an exponential - function graph.
• The fourth graph does not have a horizontal asymptote and is not an exponential - function graph.

Answer:

The first and the second graphs represent exponential functions.