##### Find the x- and y-intercepts of the rational function. (If an answer does not ex

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Find the x- and y-intercepts of the rational function. (If an answer does not exist, enter DNE.)
r(x) =
 x2 − 4 x2

x-intercept
(xy) =
−2,0

(smaller x-value)
x-intercept
(xy) =
2,0

(larger x-value)
y-intercept
(xy) =
∞,0

Jul 15th, 2015

Thank you for the opportunity to help you with your question!

$r(x)=\frac{x^2-4}{x^2}$

To find the x-intercepts, put r(x) = 0

$\\ \frac{x^2-4}{x^2}=0\\ \\ x^2-4=0\\ \\ x^2=4\\ \\ x=\pm\sqrt{4}\\ \\ x=\pm2$

So, x-intercepts are x = 2, -2

To find the y-intercepts, put x = 0

$\\ r(0)=\frac{0^2-4}{0^2}\\ \\ r(0)=\frac{-4}{0}\\$

Division by 0 is undefined.

So, there are no y-intercepts.

x-intercepts : (2,0) , (-2,0)

y-intercept  : DNE

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 15th, 2015

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Jul 15th, 2015
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Jul 15th, 2015
Oct 23rd, 2017
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