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.
-$$f ( x ) = \frac { 2 x ^ { 2 } + 2 x - 5 } { x ^ { 2 } + 2 }$$
A) a. $y = 0$
b. Graph does not cross $y = 0$.

B) a. $y = 0$
b. $\left( - \frac { 5 } { 2 } , 0 \right)$

C) a. $y = 2$
b. $\left( \frac { 9 } { 2 } , 2 \right)$

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.
-$$f ( x ) = \frac { 2 x ^ { 2 } + 2 x - 5 } { x ^ { 2 } + 2 }$$
A) a. $y = 0$
b. Graph does not cross $y = 0$.

B) a. $y = 0$
b. $\left( - \frac { 5 } { 2 } , 0 \right)$

C) a. $y = 2$
b. $\left( \frac { 9 } { 2 } , 2 \right)$

D) a. No horizontal asymptote
b. Not applicable

Quizplus · Accepted Answer

To find the horizontal asymptote of the function $f(x) = \frac{2x^2 + 2x - 5}{x^2 + 2}$, we compare the degrees of the polynomials in the numerator and the denominator. Since they are the same (degree 2), the horizontal asymptote is found by dividing the leading coefficients, which gives $y = \frac{2}{1} = 2$. To find where the graph crosses this asymptote, we set $f(x) = 2$ and solve for $x$, which gives $x = \frac{9}{2}$.

A Identify the Horizontal Asymptote (If Any) f(x)=2x2+2x−5x2+2f ( x ) = \frac { 2 x ^ { 2 } + 2 x - 5 } { x ^ { 2 } + 2 }f(x)=x2+22x2+2x−5​

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