Find the domain and vertical asymptote of $f ( x ) = - \log _ { 2 } x + 3$ .
A)Domain: $( 0 , \infty )$ Asymptote: y -axis
B)Domain: $( 0 , \infty )$ Asymptote: x=3
C)Domain: $( 3 , \infty )$ Asymptote: $x = 8.00$
D)Domain: $( - \infty , \infty )$ Asymptote: y -axis
E)Domain: $( 3 , \infty )$ Asymptote: y -axis

Question

Quizplus · Accepted Answer

The function is defined for all positive values of $x$ since the logarithm is not defined for $x \leq 0$. The vertical asymptote occurs when the argument of the logarithm approaches $0$, which means $x$ approaches $0$. This leads to the function becoming infinitely negative, but since there is a positive constant of $3$ added to the function, the asymptote will be the $y$-axis. Therefore, the answer is A.

Find the Domain and Vertical Asymptote Of f(x)=−log⁡2x+3f ( x ) = - \log _ { 2 } x + 3f(x)=−log2​x+3

Find the Domain and Vertical Asymptote Of $f ( x ) = - \log _ { 2 } x + 3$