Determine which of the rational functions given below has the following feature(s).
-x-intercepts: $( - 5,0 )$ and $( - 3,0 ) , y$-intercepts: $\left( 0 , \frac { 3 } { 5 } \right)$, vertical asymptote: $x = 5$, horizontal asymptote: $y = 1$
A) $f ( x ) = \frac { ( x - 5 ) ( x - 3 ) } { ( x + 5 ) ^ { 2 } }$

B) $f ( x ) = \frac { ( x + 5 ) ( x + 3 ) } { ( x - 5 ) ^ { 2 } }$

C) $f ( x ) = \frac { ( x - 5 ) ( x - 3 ) } { ( x + 5 ) }$

D) $f ( x ) = \frac { ( x + 5 ) ( x + 3 ) } { ( x - 5 ) }$

Question

Determine which of the rational functions given below has the following feature(s).
-x-intercepts: $( - 5,0 )$ and $( - 3,0 ) , y$-intercepts: $\left( 0 , \frac { 3 } { 5 } \right)$, vertical asymptote: $x = 5$, horizontal asymptote: $y = 1$
A) $f ( x ) = \frac { ( x - 5 ) ( x - 3 ) } { ( x + 5 ) ^ { 2 } }$

B) $f ( x ) = \frac { ( x + 5 ) ( x + 3 ) } { ( x - 5 ) ^ { 2 } }$

C) $f ( x ) = \frac { ( x - 5 ) ( x - 3 ) } { ( x + 5 ) }$

D) $f ( x ) = \frac { ( x + 5 ) ( x + 3 ) } { ( x - 5 ) }$

Quizplus · Accepted Answer

The function $f(x) = \frac{(x + 5)(x + 3)}{(x - 5)^2}$ has x-intercepts at $x = -5$ and $x = -3$ (where the numerator equals zero), a y-intercept at $\left(0, \frac{3}{5}\right)$ (substitute $x = 0$ into the function), a vertical asymptote at $x = 5$ (where the denominator equals zero), and a horizontal asymptote at $y = 1$ (since the degrees of the numerator and denominator are the same, the horizontal asymptote is the ratio of the leading coefficients, which are both 1).

Determine Which of the Rational Functions Given Below Has the Following