Given $f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }$ , determine the equations of any slant and vertical asymptote.
A)slant: y = x - 3; vertical: x = 3
B)slant: y = x + 3; vertical: x = 7
C)slant: none; vertical: none
D)slant: y = x - 11; vertical: none
E)slant: y = x + 10; vertical: x = -4

Question

Quizplus · Accepted Answer

To find the slant asymptote, divide the numerator by the denominator. The division gives $y = x + 3$ as the slant asymptote. The vertical asymptote is found by setting the denominator equal to zero, which gives $x = 7$.

Given f(x)=x2−4x+3x−7f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }f(x)=x−7x2−4x+3​

Given $f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }$