summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of…

Explanation:

Step1: Recall vertical - asymptote definition

Vertical asymptotes occur where the function is undefined and the limit approaches infinity or negative infinity. For a function of the form $y = f(x)=\frac{g(x)}{h(x)}$, vertical asymptotes are at the values of $x$ that make $h(x)=0$. The given function is $f(x)=2(4 - x)e^{x}=\frac{2(4 - x)}{e^{-x}}$. The exponential function $y = e^{-x}=\frac{1}{e^{x}}$ is defined for all real - valued $x$, i.e., $e^{-x}\neq0$ for all $x\in(-\infty,\infty)$. Also, $2(4 - x)$ is a polynomial and is defined for all real $x$.

Step2: Determine the existence of vertical asymptotes

Since both the numerator $2(4 - x)$ (a polynomial) and the denominator $e^{-x}$ (an exponential function) are defined for all real $x$, the function $f(x)=2(4 - x)e^{x}$ has no values of $x$ for which it is undefined in the real - number system. So, there are no vertical asymptotes.

Answer:

C. There are no vertical asymptotes.