the graph of $y = 3(2)^{x}$ is shown above. which of the following statements about the function over the…

the graph of $y = 3(2)^{x}$ is shown above. which of the following statements about the function over the intervals $(-\\infty,0)$ and $(0,\\infty)$ is true?\na the function is increasing over the interval $(-\\infty,0)$ and decreasing over the interval $(0,\\infty)$.\nb the function is decreasing over the interval $(-\\infty,0)$ and increasing over the interval $(0,\\infty)$.\nc the function is increasing over both intervals.\nd the function is decreasing over both intervals.

the graph of $y = 3(2)^{x}$ is shown above. which of the following statements about the function over the intervals $(-\\infty,0)$ and $(0,\\infty)$ is true?\na the function is increasing over the interval $(-\\infty,0)$ and decreasing over the interval $(0,\\infty)$.\nb the function is decreasing over the interval $(-\\infty,0)$ and increasing over the interval $(0,\\infty)$.\nc the function is increasing over both intervals.\nd the function is decreasing over both intervals.

Answer

Explanation:

Step1: Recall exponential - function properties

The general form of an exponential function is $y = a\cdot b^{x}$, where $a>0$ and $b > 1$ (in the given function $y = 3(2)^{x}$, $a = 3$ and $b=2$).

Step2: Analyze the behavior of the exponential function

For an exponential function $y=a\cdot b^{x}$ with $a>0$ and $b > 1$, the function is increasing for all real - values of $x$. That is, as $x$ increases, $y$ increases.

Answer:

C. The function is increasing over both intervals.