Question

Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.)

Answer 1

Solution:

Given the function;

$y=\frac{x^2}{x^2+48}$

The graph of the function is;

The x-intercept is;

$(0,0)$

The y-intercept is;

$(0,0)$

The relative minimum is;

$(0,0)$

The relative maximum does not exist. Thus;

$DNE=$

The points of inflection are;

$\begin{gathered} (-4,\frac{1}{4})\ldots\ldots..\ldots.smaller\text{ x-value} \\ (4,\frac{1}{4})\ldots.\ldots\ldots\ldots\text{.larger x-value} \end{gathered}$

Lastly, it has no vertical asymptote. The equation of the asymptote is;

$y=1$