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Unit Exam Review and Logarithmic Functions

Unit Exam Review and Logarithmic Functions. AII, 15.0: Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true. . Before we begin….

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Unit Exam Review and Logarithmic Functions

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  1. Unit Exam Review and Logarithmic Functions AII, 15.0: Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true.

  2. Before we begin… • Create a sheet with the exponential and logarithmic properties you will need to know for the exam. • Exponential (7) • Logarithm (3) and special properties • Inverse Property • Include the properties for graphing exponential functions. • General Equation and steps for graphing • Make sure you know how a, h, and k affect the graph • Know how to find Domain, Range, and Asymptote • By the end of today you will include the properties for graphing logarithmic properties • You have: MINUTES MAXIMUM!!!!!!!!

  3. Objectives • To be able to analyze a solution and determine where the error has occurred and how to correct it. • Graph Logarithmic equations. • Exponential functions and logarithmic functions are inverse functions; you can graph logarithmic functions using what you know about exponential graphs.

  4. Objective 1: Error Analysis • You will now use the information you have gathered • Use the information to find the errors for the given solutions • You will be given a solution • It is your job to identify the error • It is your job to provide the correction for the error

  5. Error Analysis Find and Correct the Error… Correct Procedure • Because • Because

  6. Error Analysis Find and Correct the Error… Correct Procedure • Note:

  7. Error Analysis Find and Correct the Error… Correct Procedure

  8. Error Analysis Find and Correct the Error… Correct Procedure • The distributive property incorrectly used

  9. Error Analysis Find and Correct the Error… Correct Procedure • Both sides of original equation should be in the exponent. So, should have been

  10. Objective 2: Logarithmic Functions Graphing Logarithmic Functions: • The graph of is shown where b>1. • The graph of is the reflection of the graph of in the line y=x • The graph of includes (1,0) and (b,1) • The y-axis is a vertical asymptote • The domain is x>0, and the range is all real numbers

  11. Translations Review Translating Logarithmic Functions • If |a|>1, the graph is vertically expanded • If 0<|a|<1, the graph is vertically compress • If a is negative, the graph is reflected about the x-axis • h represents an horizontal shift on the graph • k represents a vertical shift on the graph

  12. Properties of Logarithmic Function • Domain: • x>h • Range: • All real numbers • Asymptote • x=h

  13. Example 4 SOLUTION For both graphs, find the two key points where and where y 1. = • Let Then , • so is on the graph. 0 = y 0 = x x 3. 1. = = Let Then , so is on the graph. 1 = 3, 1 1, 0 ( ( ) ) y y log3 1 log3 3 = = Graph Logarithmic Functions Graph the function. Describe the vertical asymptote. State the domain and range. a. b. y log3 x y log3 x 2 ( ) = = –

  14. Example 4 b. Let Then , so is on the graph. 0 = Let Then so is on the graph. 1, = The vertical asymptote is The domain is , and the range is all real numbers. y y log3 log3 5 3 2 2 ( ( ) ) = = – – x 2 > x x x 5. 3. 2. = = = 5, 1 3, 0 ( ( ) ) Graph Logarithmic Functions The vertical asymptote is the y-axis. The domain is , and the range is all real numbers. x 0 >

  15. Checkpoint ANSWER ; domain: , range: all real numbers x 0 = x 0 > Graph Logarithmic Functions Graph the function. Describe the vertical asymptote. State the domain and range. 11. y log10 x =

  16. Checkpoint y log2 x 3 ( ) = – ANSWER ; domain: , range: all real numbers x 3 > x 3 = Graph Logarithmic Functions Graph the function. Describe the vertical asymptote. State the domain and range. 12.

  17. Checkpoint ANSWER ; domain: , range: all real numbers x 0 > x 0 = Graph Logarithmic Functions Graph the function. Describe the vertical asymptote. State the domain and range. 13. y log5 x 3 = +

  18. Conclusion Summary Assignment • On the sheet created earlier today include the properties for graphing logarithmic properties. • Minutes Max • Begin your assignment • Logarithmic Functions • Pg437 #(69-87 ODD, 82,86,89 EC) • Problems not finished will be left as homework.

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