Begin by graphing f(x)=log4x.

Question

Begin by graphing

f(x)=log4x.

Then use transformations of this graph to graph the given function. What is the vertical​ asymptote? Use the graphs to determine the given​ function's domain and range.

h(x)=4+log4x

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Part 1

Graph the function

h(x)=4+log4x.

Graph the asymptote of​ h(x) as a dashed line. Use the graphing tool to graph the function.

Part 2

What is the vertical​ asymptote?

enter your response here

​(Type an​ equation.)

Part 3

What is the domain of

h(x)=4+log4x​?

enter your response here

​(Simplify your answer. Type your answer in interval​notation.)

Part 4

What is the range of

h(x)=4+log4x​?

enter your response here

​(Simplify your answer. Type your answer in interval​notation.)

Answer 1

vertical asymptote is x=0

domain is x>0 (0, inf)

range is any real number (-inf, inf)

same for log4x as for 4+log4x

4+log4x is log4x shifted up by 4,

which doesn't change domain or range, or the asymptote