Given the logarithmic function
[tex]h(x)\text{ = }\log _4x[/tex]
The sketch of the above function is as shown below
Thus, the correct option for the sketch is D.
The domain of the h(x) function is evaluated to be
[tex]\begin{gathered} x>0 \\ in\text{ interval notation,} \\ we\text{ have (0, }\infty) \end{gathered}[/tex]
Thus, the domain of the function in interval notation is (0,∞)
Vertical asymptote of the h(x) function:
[tex]\begin{gathered} At\text{ the vertical asymptote,} \\ x=0 \end{gathered}[/tex]
Thus, the equation of the vertical asymptote is x = 0
