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

Question

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

Answer 1

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

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

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

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

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