Find the domain, range, and asymptote of the function. $g ( x ) = \log _ { 2 } ( x + 4 )$

A) Domain: $( - 4 , \infty )$
, Range: $( - 4 , \infty )$
, 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

Find the domain, range, and asymptote of the function. $g ( x ) = \log _ { 2 } ( x + 4 )$

A) Domain: $( - 4 , \infty )$
, Range: $( - 4 , \infty )$
, 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

Quizplus · Accepted Answer

The domain of $g(x) = \log_2(x + 4)$ is determined by the requirement that the argument of the logarithm, $x + 4$, must be greater than 0. Thus, $x + 4 > 0$ leads to $x > -4$, giving the domain as $(-4, \infty)$. The range of any logarithmic function is all real numbers, $(-\infty, \infty)$, because a logarithm can output any real number depending on its input. The vertical asymptote occurs where the argument of the logarithm equals zero, which is at $x = -4$, since the function is undefined at and approaches infinity as $x$ approaches $-4$ from the right.

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

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