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}} ).\nfind the domain of ( f(x) ). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the domain is all real ( x ), except ( x= ) (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= ) (type an integer or a decimal. use a comma to separate answers as needed.)\nb. there are no ( x )-intercepts.
Answer
Explanation:
Step1: Domain of the function
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 (x^{2}) is defined for all real (x). So, the domain of (f(x)) is all real (x).
Step2: X - intercepts of the function
The (x) - intercepts of a function (y = f(x)) are found by setting (y = 0). So, we set (9e^{-0.5x^{2}}=0). Since (e^{-0.5x^{2}}=\frac{1}{e^{0.5x^{2}}}), and (e^{0.5x^{2}}>0) for all real (x) (because the exponential function (y = e^{v}), where (v = 0.5x^{2}\geq0) and (e^{v}>0) for all (v\in R)), then (9e^{-0.5x^{2}}>0) for all real (x).
Answer:
For the domain: B. The domain is all real (x). For the (x) - intercepts: B. There are no (x) - intercepts.