Determine which of the rational functions given below has the following feature(s).
-x-intercepts: 4 and $1 , y$-intercepts: none, vertical asymptotes: $x = 0$ and $x = - 2$, horizontal asymptote: $\mathrm { y } = 1$
A) $f ( x ) = \frac { ( x + 4 ) ( x + 1 ) } { x ( x - 2 ) }$
B) $f ( x ) = \frac { ( x - 4 ) ( x - 1 ) } { ( x + 2 ) ^ { 2 } }$
C) $f ( x ) = \frac { ( x - 4 ) ( x - 1 ) } { x ( x + 2 ) }$
D) $f ( x ) = \frac { ( x + 4 ) ( x + 1 ) } { ( x - 2 ) }$

Question

Quizplus · Accepted Answer

Option C is correct because the numerator $(x - 4)(x - 1)$ gives x-intercepts at $x = 4$ and $x = 1$, and the denominator $x(x + 2)$ gives vertical asymptotes at $x = 0$ and $x = -2$. The degrees of the numerator and denominator are the same, leading to a horizontal asymptote at $y = 1$ when considering the leading coefficients.

Determine Which of the Rational Functions Given Below Has the Following