Given $f ( x ) = \frac { x ^ { 2 } - 10 x + 21 } { x + 5 }$ , determine the equations of any slant and vertical asymptote.
A)slant: y = x + 9; vertical: x = -12
B)slant: y = x - 15; vertical: none
C)slant: y = x + 8; vertical: x = -4
D)slant: y = x - 15; vertical: x = -5
E)slant: y = x + 8; vertical: x = -8

Question

Quizplus · Accepted Answer

The vertical asymptote occurs where the denominator is zero, which is $x = -5$. The slant asymptote is found by dividing the numerator by the denominator, resulting in $y = x - 15$.

Given f(x)=x2−10x+21x+5f ( x ) = \frac { x ^ { 2 } - 10 x + 21 } { x + 5 }f(x)=x+5x2−10x+21​

Given $f ( x ) = \frac { x ^ { 2 } - 10 x + 21 } { x + 5 }$