Question

Sketch the logarithmic function. Label three points that lie on the graph, and determine the domain and the equation of any vertical asymptotes.

Answer 1

Given the logarithmic function

`h(x)\text{ = }\log _4x`

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

`\begin{gathered} x>0 \\ in\text{ interval notation,} \\ we\text{ have (0, }\infty) \end{gathered}`

Thus, the domain of the function in interval notation is (0,∞)

Vertical asymptote of the h(x) function:

`\begin{gathered} At\text{ the vertical asymptote,} \\ x=0 \end{gathered}`

Thus, the equation of the vertical asymptote is x = 0