$\text { Match the function } f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } + 2 } \text { with one of the following graphs. }$

Question

Quizplus · Accepted Answer

The given function has a vertical asymptote at $x=\pm \sqrt{2}$, as the denominator becomes zero at these points. It also has a horizontal asymptote at $y=2$, as the degree of the numerator and the denominator are the same. Option C is the only graph that has both a vertical asymptote and a horizontal asymptote, and it also passes through the point $(0,0)$, which is the $y$-intercept of the function. Therefore, C is the best choice for the graph of the given function.

Match the function f(x)=2x2x2+2 with one of the following graphs. \text { Match the function } f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } + 2 } \text { with one of the following graphs. } Match the function f(x)=x2+22x2​ with one of the following graphs.

$\text { Match the function } f ( x ) = \frac { 2 x ^ { 2 } } { x ^ { 2 } + 2 } \text { with one of the following graphs. }$