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

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of $f(x)=9e^{-0.5x^{2}}$. b. there are no x - intercepts. find the y - intercepts of $f(x)$. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the y - intercept(s) is/are at $y = 9$. (type an integer or a decimal. use a comma to separate answers as needed.) b. there are no y - intercepts. find any horizontal asymptotes of $f(x)$. select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. a. the function has one horizontal asymptote, $□$. (type an equation.) b. the function has two horizontal asymptotes. the top asymptote is $□$ and the bottom asymptote is $□$. (type equations.) c. there are no horizontal asymptotes.

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of $f(x)=9e^{-0.5x^{2}}$. b. there are no x - intercepts. find the y - intercepts of $f(x)$. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the y - intercept(s) is/are at $y = 9$. (type an integer or a decimal. use a comma to separate answers as needed.) b. there are no y - intercepts. find any horizontal asymptotes of $f(x)$. select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. a. the function has one horizontal asymptote, $□$. (type an equation.) b. the function has two horizontal asymptotes. the top asymptote is $□$ and the bottom asymptote is $□$. (type equations.) c. there are no horizontal asymptotes.

Answer

Explanation:

Step1: Find the y - intercept

The y - intercept of a function (y = f(x)) is found by setting (x = 0). For (f(x)=9e^{-0.5x^{2}}), when (x = 0), we have (f(0)=9e^{-0.5\times0^{2}}). Since (e^{0}=1), then (f(0)=9\times1 = 9).

Step2: Find the horizontal asymptote

We use the limit (\lim_{x\rightarrow\pm\infty}f(x)). For (y = 9e^{-0.5x^{2}}), we know that (\lim_{x\rightarrow\pm\infty}- 0.5x^{2}=-\infty). And (\lim_{u\rightarrow-\infty}e^{u}=0). Let (u=-0.5x^{2}), so (\lim_{x\rightarrow\pm\infty}9e^{-0.5x^{2}}=9\times\lim_{x\rightarrow\pm\infty}e^{-0.5x^{2}} = 0).

Answer:

For the y - intercept: A. The y - intercept(s) is/are at (y = 9). For the horizontal asymptote: A. The function has one horizontal asymptote, (y = 0).