Intermediate Algebra – Student Workbook – Second Edition 2013

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

Lesson 4b – More on Logarithms Mini-Lesson Problem 6 YOU TRY – SOLVE EXPONENTIAL EQUATIONS Solve for 12.5 + 3 x = 17.8 Round the final result to three decimal places. Original Problem Statement Step 1: ISOLATE the exponential part of the equation (Hint: Start by subtracting 12.5 from both sides). Step 2: Change the equation to LOGARITHMIC form Step 3: ISOLATE the variable Step 4: IDENTIFY the final result in EXACT form then in rounded form as indicated by the problem. You may need to use Change of Base here to compute your logarithm. Step 5: CHECK your result by using the graphing (intersection) method to solve the original problem Scottsdale Community College Page 168 Intermediate Algebra
Lesson 4b – More on Logarithms Mini-Lesson Graphing and Characteristics of the Logarithmic Function The Change of Base Formula can be used to graph Logarithmic Functions. In the following examples, we will look at the graphs of two Logarithmic Functions and analyze the characteristics of each. Problem 7 WORKED EXAMPLE – GRAPHING LOGARITHMIC FUNCTIONS Given the function ( ) , graph the function using your calculator and identify the characteristics listed below. Use window x: [-5..10] and y: [-5..5]. Graphed function: To enter the function into the calculator, we need to rewrite it using the Change of Base Formula, enter that equation into Y 1 , and then Graph. ( ) Characteristics of the function: Domain: x > 0, Interval Notation: (0,∞) The graph comes close to, but never crosses the y-axis. Any value of x that is less than or equal to 0 (x ≤ 0) produces an error. Any value of x greater than 0, to infinity is valid. To the right is a snapshot of the table from the calculator to help illustrate this point. Range: All Real Numbers, Interval Notation (-∞,∞) The graph has y values from negative infinity to infinity. As the value of x gets closer and closer to zero, the value of y continues to decreases (See the table to the right). As the value of x gets larger, the value of y continues to increase. It slows, but it never stops increasing. y-intercept: Does Not Exist (DNE). The graph comes close to, but never crosses the y-axis. x-intercept: (1,0) The graph crosses the x-axis when y = 0. This can be checked by looking at both the graph and the table above as well as by entering the equation into the calculator (log(1)/log(2)) Left to Right behavior: The value of y quickly increases from -∞ to 0 as the value of x increases from just above 0 to 1 (Remember that x cannot equal 0). As the value of x increases from 1 to ∞, the value of y continues to increase (also to ∞), but at a slower and slower rate. Scottsdale Community College Page 169 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 1b - Linear Equations Practi
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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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