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# Find the x- and y- intercepts of the rational function.

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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 − 16 x2

Jun 25, 2014

#1
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x intercepts are where the y value is zero.  Therefore to find the x intercept we let y=0

x^2-16=0

x^2=16

x=4 or -4

To find y intercept we need to recognize that it occurs where x=0 so we set x to 0

y=0^2 +16

y=16

Jun 25, 2014

#1
+576
+10

x intercepts are where the y value is zero.  Therefore to find the x intercept we let y=0

x^2-16=0

x^2=16

x=4 or -4

To find y intercept we need to recognize that it occurs where x=0 so we set x to 0

y=0^2 +16

y=16

jboy314 Jun 25, 2014
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Wouldn't it be coordinates?

Jun 25, 2014
#3
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You could certainly express it in coordinates.    For the x intercept we let y =0.  Therefore, since we found x=4 of -4 the coordinates are  (4,0) or (-4,0)

similarly for y  intercept (and i just realized I mistyped my first response, it should be -16) we have coordinates (0,-16)

Jun 25, 2014
#4
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thank you so much.

Jun 25, 2014
#5
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When I see the term "rational function" I think of something like this .... r(x) = f(x) / g(x)

Do you mean this???..........

r(x) = (x^2 -16) / x^2

If so, the x intercepts that jboy314 gave are correct.......there are no y intercepts because the function does not exist when x = 0......here's the graph

Jun 25, 2014