Question

Given the function:

f(x)=(x^2+6x+5)/(x^2+3x−10)

Find the

Domain:

Vertical asymptote(s):
Hole(s):
Horizontal asymptote (if exists):

Answer 1

f(x)=(x^2+6x+5)/(x^2+3x−10)
= (x+1)(x+5(/((x+5)(x-2) )
= (x+1)/(x-2)

domain: any real value of x , x ≠ -5, 2

vertical asymptote:
x = 2

hole:
x = -5

horizontal asymptote:
y = 1

see:
http://www.wolframalpha.com/input/?i=plot+y+%3D+%28x%5E2%2B6x%2B5%29%2F%28x%5E2%2B3x−10%29+

notice the graph cannot show the hole at x = -5