Expert: Sherman D. - 1/27/2005

Question
1: Find the Domain, zeros,vertical asymptotes,and horizontal asymptotes for the following three problems: . f(x) = (x)/(x^2 + 3)

 (a)Domain: All Reals: zero x = 0:no vertical   asymptote: horizontal asymptote: y = 0
 (b)Domain: All Reals:Zero: x = 1:vertical asymptote: x=1:horizontal asymptote: y = 1: horizontal asymptote: y = 1
 (c)Domain:All Reals:zero: x = - 1:vertical asymptote: x = -1:no horizontal asymptote
 (d)Domain:All Reals:zero: x = 1/2:vertical asymptote: x = 0:Horizontal asymptote: y = - 1

2: r(x) = (x + 1)/(x^2 - 3x - 4)

(a) Domain: all reals:vertical asymptote:x = 0:no horizontal asymptote
(b)Domain: all reals except x = 4 and x = - 1:vertical asymptote: x = 4:horizontal asymptote: y = 0
(c)Domain: All reals except x = - 4 and x = 1:Vertical asymptote: x = - 4:horizontal asymptote: y = 1
(d) Domain:all reals except x = - 4 and x = 1:vertical asymptote: x = 1/4:horizontal asymptote: y = 1

3: h (x) = (x^2 - 9)/(x + 5)

 (a)Domain: all reals:zeros: x = 1/3, x = - 1/3
 (b)Domain: A;ll reals except 5:zeros: x = 2, x = - 2:
 (c)Domain:all reals except - 5:zeros: x = 3 and x = - 3
 (d)Domain: all reals except 1/5:Zeros: x = 1 and x = - 1  

Answer
1.)
going to www.calculator.com
Here is what i saw

all Real Zeros
x = 0
y = 0
horizontal asymptote : (1/2) and (-1/2)
No vertical asymptote

on b. and c. you have x = n and vertical asymptote is also x = n, and you can't have that.

-----------------------------------------------------------

2.) r(x) = (x + 1)/(x^2 - 3x - 4)

Using a graphing calculator, i get
All Real Zeros
Vertical Asymptote is x = -1 and x = 4
Horizontal Asymptote is y = 0
x = -1

So the answer is
(b)Domain: all reals except x = 4 and x = -1:vertical asymptote: x = 4:horizontal asymptote: y = 0

-----------------------------------------------------------

3.)
h(x) = (x^2 - 9)/(x + 5)

Using www.calculator.com
All real zeros
Vertical Asymptote : x = -5
x = -3 and 3

So the answer is
(c)Domain : all reals except -5 : zeros : x = ±3

± means - and +

Sorry i couldn't be of much more help.