Intermediate Algebra – Student Workbook – Second Edition 2013

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

Lesson 3a – Introduction to Exponential Functions Mini-Lesson Graph of a generic Exponential Growth Function f(x) = ab x , b > 1 Domain: All Real Numbers (all inputs) Range: f(x)>0 (only outputs bigger than 0) X-intercept: None (graph does not cross x-axis) Y-intercept: (0, a) Horizontal Asymptote: y = 0 (guiding line for the left side of the graph is the x-axis or y = 0) Left to right behavior of the function: Y-values INCREASING Graph of a generic Exponential Decay Function f(x) = ab x , 0 0 (only outputs bigger than 0) X-intercept: None (graph does not cross x-axis) Y-intercept: (0, a) Horizontal Asymptote: y = 0 (guiding line for the right side of the graph is the x-axis or y = 0) Left to right behavior of the function: Y-values DECREASING Problem 7 WORKED EXAMPLE – Examples of Exponential Functions a) f(x) = 2(3) x Initial Value, a = 2, y-intercept = (0, 2) Base, b = 3. f(x) is an exponential GROWTH function since b > 1. b) g(x) =1523(1.05) x Initial Value, a = 1523, y-intercept = (0, 1523) Base, b = 1.05. g(x) is an exponential GROWTH function since b > 1. c) h(x) = 256(0.85) x Initial Value, a = 256, y-intercept = (0, 256) Base, b = 0.85. h(x) is an exponential DECAY function since b < 1. d) k(x) = 32(0.956) x Initial Value, a = 32, y-intercept = (0, 32) Base, b = 0.956. k(x) is an exponential DECAY function since b < 1. Scottsdale Community College Page 104 Intermediate Algebra
Lesson 3a – Introduction to Exponential Functions Mini-Lesson Problem 8 YOU TRY – CHARACTERISTICS OF EXPONENTIAL FUNCTIONS Complete the table using the graphs to assist you. You should enter the graphs on your calculator as well using the screens below to help you. Functions are entered on the Y= screen Press WINDOW to change your values as shown below Press GRAPH to show the graphs f(x) = 125(1.25) x g(x) = 125(0.75) x Initial Value (a)? Base (b)? Domain? Range? X-intercept? Y-intercept? Horizontal Asymptote? Increasing or Decreasing? f(x) = 125(1.25) x g(x) = 125(0.75) x Scottsdale Community College Page 105 Intermediate Algebra
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Scottsdale Community College Interm
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Table of Contents Lesson 1a - Intro
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Lesson 1a - Introduction to Functio
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Lesson 1b - Linear Equations In the
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Lesson 1b - Linear Equations Mini-L
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Lesson 2a - Linear Functions and Ap
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Lesson 5b - Solving Quadratic Equat
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Lesson 6a - Exponents and Rational
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Lesson 6b - Rational Exponents & Ra
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Lesson 6b - Rational Exponents and
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Appendix A: You Try Answers Lesson
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Appendix A: You Try Answers You Try
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Intermediate Algebra – Student Workbook – Second Edition 2013

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