SOLUTION: 2. Find the domain, range, and asymptotes (if any) of the following functions:
a) 𝑓(𝑥) = 4𝑥+3/𝑥+2
b) 𝑓(𝑥) =𝑥+2/𝑥^2−1
c)𝑓(𝑥)=𝑥2−4𝑥+5/𝑥
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Question 1194412: 2. Find the domain, range, and asymptotes (if any) of the following functions:
a) 𝑓(𝑥) = 4𝑥+3/𝑥+2
b) 𝑓(𝑥) =𝑥+2/𝑥^2−1
c)𝑓(𝑥)=𝑥2−4𝑥+5/𝑥−3
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
assuming you have:
a)
domain:
or
Interval Notation:
(,) U (,)
range:
range of given function is equat to domain of inverse
so, find inverse of which is =>domain is or
then we say the range of (4x+3)/(x+2) is:
or
asympthotes:
Vertical:
Horizontal:
b)
domain:
or or
Interval Notation:
(,) U (,) U (,)
range:
range is where discriminant is >=0
discriminant is
in your case , ,
=>
=>
or
asympthotes:
Vertical: ,
Horizontal:
c)
domain:
or
range:
inverse is
=>discriminant
since domain of inverse is the range of original function,
range is: or
asymptotes:
Vertical:
Horizontal: (slant)
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