Chapter 8 Review
Rational Functions
Name _____________________________ Hr_____
Perform the indicated operation(s). Simplify the result.
1.) Simplify:
=
2.) Divide:
=
3.) Multiply:
=
Perform the indicated operation(s) and simplify.
4.) Add:
=
5.) Subtract:
=
6.) Add:
. Describe your steps.
Simplify the complex fractions.
7.)
8.)
Answer the following questions based on what you know about graphing rational functions.
9.) How do you write vertical asymptotes? ___________
10.) How do you write horizontal asymptotes? ____________
11.) Where in the equation do you look to find the vertical asymptote? __________________
12.) How do you find the horizontal asymptote from the equation of a simple rational function?
13.) How do you find the horizontal asymptote from the equation of a general rational function?
14.) How do you find the intercepts from the equation of any function?
15.) Given 𝑦
=
16.) Given 𝑦 =
𝑥
𝑥 2 −25
2
𝑥−1
, find the vertical asymptote(s) __________ and horizontal asymptote __________.
+ 3, find the vertical asymptote(s) __________ and horizontal asymptote __________.
17.) What is the horizontal asymptote of y =
18.) What is the horizontal asymptote of y =
19.) What is the horizontal asymptote of y =
?
?
?
A.) y = 0
B.) None
C.) y = 1
A.) y = 0
B.) None
C.) y = ¾
A.) y = 0
B.) None
C.) y = 4
Graph each function using a table of values.
20.) y =
Transformations:
Vertical asymptote(s):_____________
Horizontal asymptote: ___________
Domain:______________
Range: _______________
Intercepts: ___________
21.) y =
Vertical asymptote(s):_____________
Horizontal: ___________
Domain:______________
Range: _______________
Intercepts: ___________
22.) y =
Vertical:_____________
Horizontal: ___________
Domain:______________
Range: _______________
Intercepts: ___________
23.) y =
Vertical:_____________
Horizontal: ___________
Domain:______________
Range: _______________
Intercepts: ___________
Fill in the blanks to state the steps to solve rational equations.
1) __________________ completely first.
2) Find the ______________ _______________ _______________________.
3) ____________________ everything by the LCD.
4) Solve the resulting equation.
5) ____________________ your solution(s).
State any domain restrictions, then solve the equation. Make sure to check each solution.
24.)
25.)
26.)
27.)
28.)
29.)
Concept Review:
30.) Simplify
3
2+𝑖
.
31.) Simplify √−5(√−9 + √2).
32.) Given 𝑓(𝑥) = 3𝑥 − 2 and 𝑔(𝑥) = 𝑥 2 + 4, find (𝑔 ∘ 𝑓)(𝑥) and (𝑓 ∘ 𝑔)(𝑥). Are these functions inverses?