Algebra IIA
Unit V: Rational and Radical Functions
• Foundational Material
o Solve problems with linear functions
o Graph functions with asymptotes
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o Simplify polynomial expressions
o Solve quadratic equations and inequalities
Goal
Solve problems with variable functions
Simplify rational and radical expressions
Graph radical and rational functions
Solve rational and radical equations and inequalities
• Why?
o To further build a foundation for higher level mathematics such as pre-calculus, statistics, and business calculus
o To solve problems in other classes such as chemistry, physics, and biology
o 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 5: Radical Expressions and Rational Exponents and Solving Radical Equations
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Rewrite radical expressions by using rational exponents.
Simplify and evaluate radical expressions and expressions containing rational exponents.
Solve radical equations.
Relationship Between Rational Exponents and Radicals
Simplify the expressions that follow:
3
Radical:
27x
6
3
Exponent:
Radical:
x3
7
Exponent:
Simplify the expressions that follow:
4
16x
4
4
x8
3
3
x7 × 3 x 2
Write the expressions in simplified form.
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)
-125
4
2
3
25 × 25
5
3
42
625 4
3
73
3
5
1
64 3
2
5
116
8
8
1
3
2
3
Solving Radical Equations
( )
4
3
3
81
3
8
36 × 36
1
8
109
æ -1 ö
çç -8 3 ÷÷
è
ø
Examples: Solve the radical equations that follow.
2 x +1 = 14
5 3 4x + 3 = 15
3x - 4 = 2
6 x +10 = 42
8x + 6 = 3 x
3
3
x + 6 = 2 3 x -1
4 + x -1 = 5
35x = 5 x + 2
2x +14 = x + 3
Assignment: Page 363, 33-57 odd (Simplify each expression) and Page 381, 27-41 odd.