Algebra IIA
Unit V: Rational and Radical Functions
• Foundational Material
o Solve problems with linear functions
o Graph functions with asymptotes
o Simplify polynomial expressions
o Solve quadratic equations and inequalities
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Goal
Solve problems with variable functions
 Solve rational and radical equations and
inequalities
Simplify rational and radical expressions
Graph radical and rational functions
Why?
To further build a foundation for higher level mathematics such as pre-calculus, statistics, and business calculus
To solve problems in other classes such as chemistry, physics, and biology
Make predictions involving time, money and speed
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Key Vocabulary
Complex Fraction
Constant of Variation
Continuous Function
Direct Variation
Discontinuous Function
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Extraneous Solutions
Hole in a Graph
Inverse Variation
Inverse Function
Radical Equation
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Radical Function
Rational Equation
Rational Exponent
Rational Function
Lesson 2: Adding and Subtracting Rational Expressions
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Add and subtract rational expressions.
Simplify complex fractions.
Understand that rational expressions form a system analogous to the rational numbers, closed under
addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply,
and divide rational expressions. (CC.9-12.A.APR.7)
Warm-Up: Fill in the blank.
Direct Variation: ______________ Joint Variation: _______________Inverse Variation: __________
To add and subtract rational expressions ________________________________________________________
_________________________________________________________________________________________.
3x - 4 2x + 5
+
x+3 x +3
6x + 5 3x -1
+ 2
2
x -3 x -3
3x 2 - 5 2x 2 - 3x - 2
3x -1
3x -1
x -1
x
+
x 2 + 3x + 2 x +1
x
-18
+ 2
x+3 x -9
3x
3x - 2
+
2x - 2 3x - 3
2x 2 -16 x + 4
2
x+2
x -4
3x - 2
2
2x + 5 5x - 2
2 x
+
x 4
x +1
x
x +1
x 2 -1
x
x -1
You try:
x-3 x-2
+
x+4 x+4
3x - 4 6x +1
x 2 +1 x 2 +1
x -3
2x
+
x 2 + 3x - 4 x + 4
2x 2 - 30 x + 5
2
x+3
x -9
x+2
x -1
x -3
x +5
3 x
+
x 2
x -1
x
Assignment: Page 332, 17, 19, 23-29 odd, 31-41 odd, 43, 45.