Question

F(x)=x^2/X^2-9 Find X and y intercepts. Vertical Asymptotes and horizontal Asymptotes

Answer 1

\[\frac{x^2}{x^2 - 9} = \frac{x^2}{(x+3)(x-3)}\]
Denominator is zero when x=3 or x=-3
Vertical Asymptotes at x=3 and x=-3
Horizontal Asymptote is y=1 because its the same degree on top and bottom
Also if you used polynomial division here, the quotient is 1+(9/x^2-9) the remainder will get closer and closer to zero as x gets larger, so the function approaches y=1
Y-intercept: find f(0). f(0) = 0, so y-intercept is (0,0)
X-intercept: solve for x when f(x) = 0
x^2 = 0 --> x= 0, so x-intercept is also (0,0)