Find the domain, range, and asymptote of the function. $g ( x ) = 2 + \log _ { 2 } ( x + 4 )$
A) Domain: $( - 4 , \infty )$
, Range: $( 2 , \infty )$
, Asymptote: $x = - 4$
B) Domain: $( 4 , \infty )$
, Range: $( 4 , \infty )$
, Asymptote: $x = 4$
C) Domain: $( - 4 , \infty )$
, Range: $(-\infty, \infty )$
, Asymptote: $x = - 4$
D) Domain: $( - 4 , \infty )$
, Range: $( - 4 , \infty )$
, Asymptote: $x = 4$
E) none of these

Question

Quizplus · Accepted Answer

The logarithmic function $\log_2(x+4)$ is defined for $x+4 > 0$, which gives the domain as $x > -4$, or $(-4, \infty)$. The range of any logarithmic function is all real numbers, $(-\infty, \infty)$, because as $x$ approaches the vertical asymptote from the right, the logarithm approaches $-\infty$, and as $x$ goes to $\infty$, the logarithm goes to $\infty$. The vertical asymptote is where the argument of the logarithm, $x+4$, equals zero, which is at $x = -4$.

Find the Domain, Range, and Asymptote of the Function g(x)=2+log⁡2(x+4)g ( x ) = 2 + \log _ { 2 } ( x + 4 )g(x)=2+log2​(x+4)

Find the Domain, Range, and Asymptote of the Function $g ( x ) = 2 + \log _ { 2 } ( x + 4 )$