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)=lnleft(x^{2}+36\right) ).\noa. the domain is all real ( x ), except ( x= ).\n(use a comma to separate answers as needed.)\nob. the domain is all real numbers.\nfind the ( x )-intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\noa. the ( x )-intercept(s) is (are) ( x= )\n(round to one decimal place as needed. use a comma to separate answers as needed.)\nob. there are no ( x )-intercepts.\nfind the ( y )-intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\noa. the ( y )-intercept(s) is (are) ( y= )\n(round to one decimal place as needed. use a comma to separate answers as needed.)\nob. there are no ( y )-intercepts.

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of ( f(x)=lnleft(x^{2}+36\right) ).\noa. the domain is all real ( x ), except ( x= ).\n(use a comma to separate answers as needed.)\nob. the domain is all real numbers.\nfind the ( x )-intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\noa. the ( x )-intercept(s) is (are) ( x= )\n(round to one decimal place as needed. use a comma to separate answers as needed.)\nob. there are no ( x )-intercepts.\nfind the ( y )-intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice.\noa. the ( y )-intercept(s) is (are) ( y= )\n(round to one decimal place as needed. use a comma to separate answers as needed.)\nob. there are no ( y )-intercepts.

Answer

Explanation:

Step1: Find the domain

For the function (y = \ln(u)), the argument (u=x^{2}+36). Since (x^{2}\geq0) for all real (x), then (x^{2}+36\geq36>0) for all real (x). So the domain is all real numbers.

Step2: Find the (x -) intercept

Set (y = 0), so (\ln(x^{2}+36)=0). Using the property (\ln(a)=b\Leftrightarrow a = e^{b}), we have (x^{2}+36=e^{0}=1). Then (x^{2}=1 - 36=- 35). Since (x^{2}=-35) has no real solutions, there are no (x -) intercepts.

Step3: Find the (y -) intercept

Set (x = 0). Then (y=\ln(0^{2}+36)=\ln(36)\approx3.6) (using a calculator, (\ln(36)=\ln(6^{2}) = 2\ln(6)\approx2\times1.792 = 3.584\approx3.6))

Answer:

For the domain: B. The domain is all real numbers. For the (x -) intercept: B. There are no (x -) intercepts. For the (y -) intercept: A. The (y -) intercept(s) is (are) (y = 3.6)