a. Identify the horizontal asymptote (if any).
b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the
horizontal asymptote.
-$$s ( x ) = \frac { 5 x - 10 } { x ^ { 2 } + 5 x - 4 }$$
A) a. $y = 0$
b. $\left( - \frac { 5 } { 2 } , 0 \right)$

B) a. $y = 2$
b. $( 0,2 )$

C) a. $y = 0$
b. $( 2,0 )$

D) a. No horizontal asymptote
b. Not applicable

Question

a. Identify the horizontal asymptote (if any).
b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the
horizontal asymptote.
-$$s ( x ) = \frac { 5 x - 10 } { x ^ { 2 } + 5 x - 4 }$$
A) a. $y = 0$
b. $\left( - \frac { 5 } { 2 } , 0 \right)$

B) a. $y = 2$
b. $( 0,2 )$

C) a. $y = 0$
b. $( 2,0 )$

D) a. No horizontal asymptote
b. Not applicable

Quizplus · Accepted Answer

The horizontal asymptote of a rational function is determined by comparing the degrees of the polynomial in the numerator and the denominator. Since the degree of the numerator (1) is less than the degree of the denominator (2), the horizontal asymptote is $y = 0$. To find where the graph crosses this asymptote, set $s(x) = 0$ and solve for $x$: $5x - 10 = 0$, which gives $x = 2$. Therefore, the graph crosses the horizontal asymptote at $(2,0)$.

A Identify the Horizontal Asymptote (If Any) s(x)=5x−10x2+5x−4s ( x ) = \frac { 5 x - 10 } { x ^ { 2 } + 5 x - 4 }s(x)=x2+5x−45x−10​

A Identify the Horizontal Asymptote (If Any) $s ( x ) = \frac { 5 x - 10 } { x ^ { 2 } + 5 x - 4 }$