Question

The function has a vertical asymptote of x=2 The function has a removable discontinuity of x=-2 The function has a horizontal asymptote of y= 0 No x intercept Y-intercept is (0,-0.5) End Behavior f(x) --> 0, x? -oo f(x) ? 0, x ? oo

What is the rational function? Please help!!
( ‘oo’ is infinity btw)

Answer 1

come on, just follow the steps:
<u>vertical asymptote of x=2</u>
y = 1/(x-2)

<u>removable discontinuity of x=-2</u>
y = (x+2)/((x-2)(x+2))

<u>horizontal asymptote of y= 0</u>
no adjustment needed, since the degree below is greater than that above

<u>No x intercept</u>
still no adjustment needed, since everywhere except x = -2, y = 1/(x-2), which has no x-intercept.

<u>y-intercept is (0,-0.5)</u>
(x+2)/((x-2)(x+2)) = 2/-4 = -0.5 at x=0, so we are done.