Identify an asymptote of the function h(x)=2log8(x−3)

Question

.(1 point)
Responses

x = 1
x = 1

x = 3
x = 3

x = 2
x = 2

x = 4

Answer 1

To find the asymptote of the function \( h(x) = 2 \log_8(x - 3) \), we need to identify the values of \( x \) for which the function is undefined.

The logarithmic function is only defined for positive arguments, so we need to set the argument of the logarithm greater than zero:

\[ x - 3 > 0 \]

Solving this inequality gives:

\[ x > 3 \]

Thus, the function \( h(x) \) is defined for \( x > 3 \) and is undefined for \( x \leq 3 \). This means that there is a vertical asymptote at:

\[ x = 3 \]

So, the correct response is:

x = 3.