AP test problems, Derivatives and Tangent lines

[chris40256]

Homework Statement

Let f be the function given by f(x) = (2x-5)/(x^2-4).
a.Find the domain of f.
b.Write an equation for each vertical and each horizontal asymptote for the graph of f.
c.Find f'(x).
d.Write an equation for the line tangent to the graph of f at the point (0,f(0)).

The Attempt at a Solution

Note: Just checking answers!
a.domain: x does not equal 2 or -2 because those values of x make the denominator 0
b. vertical asymptote
x = 2, x = -2
horizontal asymptote
as x goes to positive or negative infinity
f(x) goes to 0
y = 0

c. f'(x) = (2(x^2 - 4) - (2x - 5)(2x))/(x^2-4)^2
= (2x^2 - 8 - 4x^2 + 10x)/(x^2-4)^2
= -2(x^2 - 5x + 4)/(x^2-4)^2
= -2(x-4)(x-1)/(x^2-4)^2
f(0) = -5/(-4) = 5/4

d. y - 5/4 = slope (x - 0)
slope = f'(0) = -2(-4)(-1)/(-4)^2 = -8/16 = -1/2
y - 5/4 = (-1/2)x
y = (-1/2)x + 5/4

 

[fresh_42]

This is all correct.

https://www.wolframalpha.com/input?i=f(x)+=+(2x-5)/(x^2-4)