2 6find the following For each of the rational functions giv

2- 6,find the following, For each of the rational functions given below in numbers a. The Domain written in set builder notation (2pts) b. Vertical Asymptote(s) if any (4pts) c. Horizontal Asymptote if any (2pts) Note: Points will be deducted for answers not placed in the blank spaces given. f(x) x2-9

Solution

Solution:

2. f(x) = 4x²/(x²-9)

(a) The domain of a function is the set of input or argument values for which the function is real and defined

we find singular points

x²-9 = 0

x = 3 and x =-3
function is defined for

x<-3 and x>-3 and x>3 and x<3

domain = (-,-3) (-3,3 ) ( 3 ,)

(b) Vertical Asymptote

all zeros of denominator are the vertical asymptote

(x²-9) = 0

x = 3 and x = -3

are vertical asymptote

(c) Horizontal asymptote

as we can see that degree of numerator and denominator both are same

thus

asymptote = numerator leading coffi. / denominator leading coffi. = 4/1 = 4

HA = 4

Answer