calculus graph, please check, thanx

Qu.

Use graph sketching strategy to sketch the graph of the function f(x) = 4x -15/ x^2 -9

__Step 1__ The domain of f is all natural numbers except + 3 or - 3 when x^2 - 9 = 0

__Step 2__ Function f in nether even or odd

__step 3 __ x intercept , 4x -15 = 0, x = 3 3/4

y intercept f (0) = 5/3

step 4

f(x) = 4x -15/ (x-3) (x+3)

f is positive (3 3/4, infinite), and negative on (-infinite, -3), (-3,3), and (3, 3 3/4)

Step 5

the derivative of f(x) = -4x^2 -36 +30x/ (x^2-9)^2

Then I got stuck....please help

ThePerfectHacker- thanks, continued

Horizontal asymptote

y = 0 ?

When m < n, the horizontal asymptote is the line y = 0

where m is the degree of polynomial in the numerator and n is the degree of polynomial in the denominator.

ThePerfectHacker - Graph of a function

Found derivative of f

= (-4x +6)(x-6)/(x^2-9)^2

Problems establishing when f is increasing or decreasing and if any stationary points