Find the x intercept of the rational function

Question

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

r(x)= x² - 9

x²

x-intercept (x, y)= (smaller x-value)

x-intercept (x, y)= (larger x-value)

y-intercept (x, y)= Does Not Exist

Answer 1

So remember, the x-intercepts and y-intercept occur when the graph touches the x and y axis respectively. An easy way to find these is just to plug in zero for the other variable.

X intercepts

For these, we'll set y or f(x) equal to zero.

0 = x² - 9

0 = (x+3)(x-3)

x+3=0 or x-3=0

x=-3 or x=3

Then put in that y value of zero to give the x-intercept points: The x-intercepts are (-3, 0) and (3,0).

Y intercept

This one is a bit simpler as we just plug in x=0 and y is basically solved already.

y = 0² - 9 = -9

The put x=0 to make the coordinate point: The y-intercept is (0, -9).