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}} ).\na. the domain is all real ( x ), except ( x = ).\n(type an integer or a decimal. use a comma to separate answers as needed.)\nb. the domain is all real ( x ).\nfind the ( x )-intercepts of ( f(x) ). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the ( x )-intercept(s) is/are at ( x = ).\n(type an integer or a decimal. use a comma to separate answers as needed.)\nb. there are no ( x )-intercepts.\nfind the ( y )-intercepts of ( f(x) ). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the ( y )-intercept(s) is/are at ( y = ).\n(type an integer or a decimal. use a comma to separate answers as needed.)\nb. there are no ( y )-intercepts.

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of ( f(x)=9e^{-0.5x^{2}} ).\na. the domain is all real ( x ), except ( x = ).\n(type an integer or a decimal. use a comma to separate answers as needed.)\nb. the domain is all real ( x ).\nfind the ( x )-intercepts of ( f(x) ). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the ( x )-intercept(s) is/are at ( x = ).\n(type an integer or a decimal. use a comma to separate answers as needed.)\nb. there are no ( x )-intercepts.\nfind the ( y )-intercepts of ( f(x) ). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the ( y )-intercept(s) is/are at ( y = ).\n(type an integer or a decimal. use a comma to separate answers as needed.)\nb. there are no ( y )-intercepts.

Answer

Explanation:

Step1: Find the domain

For the function (y = 9e^{-0.5x^{2}}), the exponential function (e^{u}) is defined for all real values of (u). Here (u=-0.5x^{2}), and since (x^{2}) is defined for all real (x), the domain of (y = 9e^{-0.5x^{2}}) is all real (x).

Step2: Find the (x -)intercepts

Set (y = 0), so (9e^{-0.5x^{2}}=0). We know that (e^{-0.5x^{2}}=\frac{1}{e^{0.5x^{2}}}), and (e^{0.5x^{2}}>0) for all real (x). Then (9e^{-0.5x^{2}}>0) for all real (x). So there are no (x -)intercepts.

Step3: Find the (y -)intercepts

Set (x = 0), then (y=9e^{-0.5\times0^{2}}). Since (e^{0}=1), we have (y = 9\times1=9).

Answer:

For the domain: B. The domain is all real (x). For the (x -)intercepts: B. There are no (x -)intercepts. For the (y -)intercepts: A. The (y -)intercept(s) is/are at (y = 9).