Select the correct graph of the following function. $$f ( x ) = \frac { x ^ { 2 } } { 2 x + 1 }$$

Question

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The function is undefined at $x=-\frac{1}{2}$, which is a vertical asymptote. The graph should have a vertical asymptote at $x=-\frac{1}{2}$. We can also note that $f(0)=0$, and as $x$ becomes very large in either direction the function approaches the line $y=\frac{1}{2}x$, which narrows down the options to only (B) and (C). In (C), the graph appears to curve downwards on the right side of the vertical asymptote, which is not consistent with the behavior described. Therefore, the correct graph is (B).

Select the Correct Graph of the Following Function f(x)=x22x+1f ( x ) = \frac { x ^ { 2 } } { 2 x + 1 }f(x)=2x+1x2​

Select the Correct Graph of the Following Function $f ( x ) = \frac { x ^ { 2 } } { 2 x + 1 }$