ca_m7_handouts - MAC 1105 Module 7 Additional Equations and...

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1 Rev.S08 MAC 1105 Module 7 Additional Equations and Inequalities Rev.S08 2 Learning Objectives Upon completing this module, you should be able to: 1. Use properties of rational exponents (rational powers). 2. Understand radical notation. 3. Solve equations involving rational powers. 4. Solve radical equations. 5. Solve absolute value equations 6. Solve inequalities involving absolute values. 7. Solve quadratic inequalities. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. 3 Rev.S08 Let’s Review Some Properties of Rational Exponents http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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2 4 Rev.S08 Let’s Practice Some Simplification http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Simplify each expression by hand. 8 2/3 b) (–32) –4/5 Solutions 5 Rev.S08 What are Power Functions? http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Power functions typically have rational exponents . A special type of power function is a root function . Examples of power functions include: f 1 ( x ) = x 2 , f 2 ( x ) = x 3/4 , f 3 ( x ) = x 0.4 , and f 4 ( x ) = 6 Rev.S08 What are Power Functions? (Cont.) http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Often, the domain of a power function f is restricted to nonnegative numbers . Suppose the rational number p/q is written in lowest terms. The domain of f ( x ) = x p/q is all real numbers whenever q is odd and all nonnegative numbers whenever q is even .
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