Find the domain of the function and identify any vertical and horizontal asymptotes.
$f ( x ) = \frac { 7 + x } { 7 - x }$
A)Domain: all real numbers x except x = 7Vertical asymptote: x = 7Horizontal asymptote: y = -1
B)Domain: all real numbers xVertical asymptote: x = -7Horizontal asymptote: y = 0
C)Domain: all real numbers x except x = 0Vertical asymptote: x = 0Horizontal asymptote: y = -1
D)Domain: all real numbers x except x = 7Vertical asymptote: x = 0Horizontal asymptote: y = -7
E)Domain: all real numbers x except x = -7Vertical asymptote: x = 0Horizontal asymptote: y = 7

Question

Find the domain of the function and identify any vertical and horizontal asymptotes. 
$f ( x ) = \frac { 7 + x } { 7 - x }$  
A)Domain: all real numbers x except x = 7Vertical asymptote: x = 7Horizontal asymptote: y = -1
B)Domain: all real numbers xVertical asymptote: x = -7Horizontal asymptote: y = 0
C)Domain: all real numbers x except x = 0Vertical asymptote: x = 0Horizontal asymptote: y = -1
D)Domain: all real numbers x except x = 7Vertical asymptote: x = 0Horizontal asymptote: y = -7
E)Domain: all real numbers x except x = -7Vertical asymptote: x = 0Horizontal asymptote: y = 7

Quizplus · Accepted Answer

The domain of the function $f(x) = \frac{7 + x}{7 - x}$ excludes the value for which the denominator is zero, which is $x = 7$. This also means there is a vertical asymptote at $x = 7$. For the horizontal asymptote, as $x$ approaches infinity, the function approaches the ratio of the leading coefficients of the numerator and the denominator, which is $\frac{1}{-1} = -1$, so the horizontal asymptote is $y = -1$.

Find the Domain of the Function and Identify Any Vertical f(x)=7+x7−xf ( x ) = \frac { 7 + x } { 7 - x }f(x)=7−x7+x​

Find the Domain of the Function and Identify Any Vertical $f ( x ) = \frac { 7 + x } { 7 - x }$