Algebra-2

Let's analyze the function step by step.

Identify the vertical asymptote

A logarithmic function has a vertical asymptote where its argument is zero, because the logarithm of zero is undefined. In this case, the argument is , and the function becomes undefined when , or .

Thus, has a vertical asymptote at .

Identify the horizontal asymptote

The horizontal asymptote of a logarithmic function can be determined by considering its behavior as or .

As , the value of increases without bound (i.e., ).

As , the value of , and there is no horizontal asymptote.

Is always negative?

For , when ,

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