select the correct answer from each drop - down menu. complete the statement to correctly describe the end…

Answer:

The left - end approaches $\infty$, and the right - end approaches $0$.

Explanation:

Step1: Analyze left - end behavior

As $x\to-\infty$, for the function $y = a\cdot b^{x}$ ($a = 10$, $b=0.75$), when $x$ is a large negative number, say $x=-n$ where $n$ is a large positive number, then $f(x)=10(0.75)^{-n}=10(\frac{1}{0.75})^{n}$. Since $\frac{1}{0.75}=\frac{4}{3}>1$, as $n\to\infty$, $10(\frac{4}{3})^{n}\to\infty$.

Step2: Analyze right - end behavior

As $x\to\infty$, for the function $y = a\cdot b^{x}$ with $0 < b=0.75<1$ and $a = 10$, when $x$ is a large positive number, $b^{x}$ gets smaller and smaller. Mathematically, $\lim_{x\to\infty}10(0.75)^{x}=0$.