Determine which of the rational functions given below has the following feature(s).
-x-intercepts: $( - 5,0 )$ and $( 2,0 )$, $y$-intercepts: none, vertical asymptotes: $x = 0$ and $x = 1$, horizontal asymptote: $y = 1$
A) $f ( x ) = \frac { ( x + 5 ) ( x - 2 ) } { x ( x - 1 ) }$

B) $f ( x ) = \frac { ( x + 5 ) ( x - 2 ) } { ( x - 1 ) ^ { 2 } }$

C) $f ( x ) = \frac { ( x - 5 ) ( x + 2 ) } { x ( x + 1 ) }$

D) $f ( x ) = \frac { ( x - 5 ) ( x + 2 ) } { ( x + 1 ) }$

Question

Determine which of the rational functions given below has the following feature(s).
-x-intercepts: $( - 5,0 )$ and $( 2,0 )$, $y$-intercepts: none, vertical asymptotes: $x = 0$ and $x = 1$, horizontal asymptote: $y = 1$
A) $f ( x ) = \frac { ( x + 5 ) ( x - 2 ) } { x ( x - 1 ) }$

B) $f ( x ) = \frac { ( x + 5 ) ( x - 2 ) } { ( x - 1 ) ^ { 2 } }$

C) $f ( x ) = \frac { ( x - 5 ) ( x + 2 ) } { x ( x + 1 ) }$

D) $f ( x ) = \frac { ( x - 5 ) ( x + 2 ) } { ( x + 1 ) }$

Quizplus · Accepted Answer

Option A correctly matches all the given features: the numerator $(x+5)(x-2)$ gives x-intercepts at $x=-5$ and $x=2$, the denominator $x(x-1)$ provides vertical asymptotes at $x=0$ and $x=1$, and the degrees of the numerator and denominator are the same, leading to a horizontal asymptote at $y=1$, as the leading coefficients of the numerator and denominator are both 1.

Determine Which of the Rational Functions Given Below Has the Following