Determine which of the rational functions given below has the following feature(s).
-$x$-intercepts: $( 4,0 )$ and $( - 3,0 )$, $y$-intercepts: none, vertical asymptotes: $x = 0$ and $x = 1$, horizontal asymptote: $y = 1$
A) $f ( x ) = \frac { ( x - 4 ) ( x + 3 ) } { x ( x - 1 ) }$
B) $f ( x ) = \frac { ( x - 4 ) ( x + 3 ) } { ( x - 1 ) ^ { 2 } }$
C) $f ( x ) = \frac { ( x + 4 ) ( x - 3 ) } { ( x + 1 ) }$
D) $f ( x ) = \frac { ( x + 4 ) ( x - 3 ) } { x ( x + 1 ) }$

Question

Quizplus · Accepted Answer

Option A is correct because the numerator $(x-4)(x+3)$ gives the $x$-intercepts at $x=4$ and $x=-3$, the denominator $x(x-1)$ gives the vertical asymptotes at $x=0$ and $x=1$, and since the degrees of the numerator and denominator are the same, the horizontal asymptote is $y=1$, which matches the coefficients of the leading terms in the numerator and denominator.

Determine Which of the Rational Functions Given Below Has the Following