CCGPS Advanced Algebra – Unit 3
Rational and Radical Functions
Dear Parents,
In this unit, students will explore two more types of families of functions – radical and rational functions. They will
also learn how to simplify expressions and solve equations and inequalities that involve rational and radical
expressions. Below you find will several resources that can be used to help support the learning for your child.
By the end of the unit, students will be able to…
- Rewrite rational expressions in different forms.
- Add, subtract, multiply, and divide rational expressions.
- Solve rational and radical equations.
- Solve rational inequalities.
- Graph rational and radical functions and identify key characteristics.
- Interpret solutions to graphs and equations given the context of the problem.
Important Vocabulary
Asymptote
Coefficient
Equation
Expression
Extraneous Solution
Inequality
Polynomial
Radical Function
Rational Function
Variable
Resources:
Textbook:
Holt McDougal – Advanced Algebra – Unit 3, Modules 6 and 7
Video Resources - Khan Academy:
Simplifying Rational Expressions - video
Adding and Subtracting Rational Expressions - video
Multiplying and Dividing Rational Expressions - video
Solving Rational Equations - video
Solving Rational Inequalities - video
Graphing Rational Functions - video
Simplifying Radical Expressions - video
Radical Equations - video
Graphing Radical Functions - video
Sample Problems
Operations with Rational Expressions and Equations
Simplify each expression or solve each equation or inequality.
1a.
x4
2x

2
x  x  12 x  4
1b.
x  12 3 x  2

2x  5 2x  5
1c.
4 x  16 x 2  2 x  3
2x  6
x4
1d.
5 x 6 10 x 2

y
x2y
1e.
4
1

x 4 x 2
1f.
7
 5
x3
2
CCGPS Advanced Algebra – Unit 3
Rational and Radical Functions
Graphs and Characteristics of Rational Functions
2. f  x  
x 2  4x  5
x 1
a. Zeros:
_____________________________________________________________
b. Vertical asymptote:
_____________________________________________________________
c. Horizontal asymptote:
_____________________________________________________________
d. Graph.
Operations with Radical Expressions and Equations
Solve each equation.
3a.
x 4 3 x
1
3b. 4  x  12 3  16
3c.
14 x  2  x  3
Graphs and Characteristics of Radical Functions
4. Graph: f  x   3 x  1. State Domain and Range.
5.
f(x) is a radical function whose domain is
(-∞, 5] and whose range is (-∞, 0], and
g(x) = x  5  2 . Which statement is true
for both f(x) and g(x)?
A. g(x) has a higher y-intercept than f(x)
B. g(x) has a greater zero than f(x)
C. The functions have the same domain.
D. The functions have the same range.
CCGPS Advanced Algebra – Unit 3
Rational and Radical Functions