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

Explanation:

Step1: Find y - intercept

Set (x = 0) in (y=f(x)=2(4 - x)e^{x}). Then (y=2(4-0)e^{0}=2\times4\times1 = 8).

Step2: Find horizontal asymptotes

We know that (\lim_{x\rightarrow+\infty}2(4 - x)e^{x}). Using L - H rule on (\lim_{x\rightarrow+\infty}\frac{4 - x}{e^{-x}}), differentiating numerator and denominator gives (\lim_{x\rightarrow+\infty}\frac{- 1}{-e^{-x}}=\lim_{x\rightarrow+\infty}e^{x}=+\infty). And (\lim_{x\rightarrow-\infty}2(4 - x)e^{x}), since (\lim_{x\rightarrow-\infty}e^{x}=0) and (\lim_{x\rightarrow-\infty}(4 - x)=+\infty), but the exponential decay of (e^{x}) dominates, so (\lim_{x\rightarrow-\infty}2(4 - x)e^{x}=0). So (y = 0) is a horizontal asymptote.

Step3: Find vertical asymptotes

The function (y = 2(4 - x)e^{x}) is a product of a polynomial (2(4 - x)) and an exponential function (e^{x}). Since (e^{x}) is defined for all real - valued (x) and the polynomial (2(4 - x)) is also defined for all real (x), there are no values of (x) for which the function is undefined. So there are no vertical asymptotes.

Answer:

A. The y - intercept(s) is/are at (y = 8). A. The function has one horizontal asymptote, (y = 0). C. There are no vertical asymptotes.