Question

select the correct answer. graph the given function. $f(x)=7^{x}$ which key features apply to the graph? a. the graph has an asymptote at $y = 0$ and is decreasing as $x$ approaches positive infinity. b. the graph has an asymptote at $y = 7$ and is decreasing as $x$ approaches positive infinity. c. the graph has an asymptote at $y = 0$ and is increasing as $x$ approaches positive infinity. d. the graph has an asymptote at $y = 7$ and is increasing as $x$ approaches positive infinity.

Explanation:

Step1: Recall exponential - function properties

The general form of an exponential function is $y = a^x$, where $a>0,a
eq1$. For the function $f(x)=7^x$, since $a = 7>1$.

Step2: Analyze the asymptote

For any exponential function of the form $y = a^x$ ($a>0,a
eq1$), the horizontal asymptote is $y = 0$.

Step3: Analyze the behavior as $x

ightarrow+\infty$
When $a>1$ in the function $y = a^x$, as $x$ approaches positive infinity, the function value $y$ increases. So for $f(x)=7^x$, as $x
ightarrow+\infty$, $y = 7^x$ increases.

Answer:

C. The graph has an asymptote at $y = 0$ and is increasing as $x$ approaches positive infinity.