Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point.
-$f ( x ) = \frac { x ^ { 2 } + 16 x + 63 } { x ^ { 2 } + 15 x + 56 }$
A)-7: hole; -8: vertical asymptote
B)-7: hole; -9: vertical asymptote
C)-8: vertical asymptote
D)7: hole; 8: vertical asymptote

Question

Quizplus · Accepted Answer

First, factor both the numerator and the denominator: $f(x) = \frac{(x+7)(x+9)}{(x+7)(x+8)}$. The factor $x+7$ cancels out, indicating a hole at $x = -7$. The denominator has a factor of $x+8$ that does not cancel, indicating a vertical asymptote at $x = -8$.

Find All Points of Discontinuity, and Determine Whether There Is f(x)=x2+16x+63x2+15x+56f ( x ) = \frac { x ^ { 2 } + 16 x + 63 } { x ^ { 2 } + 15 x + 56 }f(x)=x2+15x+56x2+16x+63​

Find All Points of Discontinuity, and Determine Whether There Is $f ( x ) = \frac { x ^ { 2 } + 16 x + 63 } { x ^ { 2 } + 15 x + 56 }$