Skills Practice Skills Practice for Lesson 7.1

Transcription

1 Skills Practice Skills Practice for Lesson.1 Name Date What s the Inverse of an Eponent? Logarithmic Functions as Inverses Vocabulary Write the term that best completes each statement. 1. The of a number to a given base is the power or eponent to which the base must be raised in order to produce the number.. A(n) is a function involving a logarithm. 3. A(n) is a logarithm with base 10.. A(n) is a logarithm with base e. Chapter l Skills Practice 569

2 Problem Set Graph each eponential function f() and the line y, and label each graph. Complete the tables for each eponential function and its inverse. Then plot each point on the grid provided. Connect the points of f 1 () with a smooth curve. Then label the graph as f 1 (). 1. f() f() f 1 () y 16 1 f() = X y = f 1 () Chapter l Skills Practice

3 Name Date. f() 5 f() 5 f 1 () Chapter l Skills Practice 51

4 3. f() 6 f() 6 f 1 () Chapter l Skills Practice

5 Name Date. f() ( 1 ) 3 f() ( 1 ) f 1 () Chapter l Skills Practice 53

6 5. f() ( 1 3 ) 3 f() ( 1 3 ) f 1 () Chapter l Skills Practice

7 Name Date 6. f() ( 1 ) f() ( 1 ) f 1 () Chapter l Skills Practice 55

8 The graph of the function h() b and the line y are shown. Sketch the graph of h 1 ().. y. h() y = 6 y 6 h() y = h 1 () y 10. h() 6 y = h() y 6 y = h() 6 y 1. 6 y = 6 h() y 6 6 y = Chapter l Skills Practice

9 Skills Practice Skills Practice for Lesson. Name Date Do I Have the Right Form? Eponential and Logarithmic Forms Problem Set Write each eponential equation as a logarithmic equation using the definition of logarithms log ( 1 ) ( 1 3 ) ( 1 6 ) ( 3 5 ) ,000 Chapter l Skills Practice 5

10 Write each logarithmic equation as an eponential equation using the definition of logarithms. 1. log log log log log log log log log l og log log Evaluate each logarithmic epression without using a calculator. Eplain how you calculated each. 9. log log 6 3 9, so log log 1 3. log 10, log log log log 5 100,000 5 Chapter l Skills Practice

11 Name Date Evaluate each logarithmic epression. Use a calculator if necessary. 3. log log log log log 00. log 1 3. log 5.5. log 100, ln ln. ln 0.. In e 1 9. ln ln 3 100, ln 5. ln log log 55. log In e 5 5. In log ln In 30 Chapter l Skills Practice 59

12 50 Chapter l Skills Practice

13 Skills Practice Skills Practice for Lesson.3 Name Date It s All in the Graph Graphs of Logarithmic Functions Problem Set Graph each function f() for y-values between 0 and 100 and then again for y-values between 0 and Describe the similarities and differences between the graphs. 1. f() 100 y 1000 y Each graph has an asymptote at y 0 and increases very rapidly.. f() 3 Chapter l Skills Practice 51

14 3. f(). f() ( 1 ) 5 Chapter l Skills Practice

15 Name Date 5. f() ( 1 3 ) 6. f() e Chapter l Skills Practice 53

16 Graph each logarithmic function. Label the coordinates of three points. Give the domain, range, intercepts, and asymptotes of the graph. Then give the -values for which the function is increasing or decreasing.. f() log y Domain: all non-negative real numbers Range: all real numbers Intercept(s): -intercept at 1, no y-intercepts (1, 0) 1 10, 1 1 ( ) (10, 1) 9 Asymptote(s): vertical asymptote at the y-ais, or 0 -values for which the function is increasing or decreasing: increasing over the entire domain. f() log Domain: Range: Intercept(s): Asymptote(s): -values for which the function is increasing or decreasing: 5 Chapter l Skills Practice

17 Name Date 9. f() log 3 Domain: Range: Intercept(s): Asymptote(s): -values for which the function is increasing or decreasing: 10. f() log Domain: Range: Intercept(s): Asymptote(s): -values for which the function is increasing or decreasing: Chapter l Skills Practice 55

18 11. f() In Domain: Range: Intercept(s): Asymptote(s): -values for which the function is increasing or decreasing: 1. f() log 1 Domain: Range: Intercept(s): Asymptote(s): -values for which the function is increasing or decreasing: 56 Chapter l Skills Practice

19 Name Date 13. f() log 1 3 Domain: Range: Intercept(s): Asymptote(s): -values for which the function is increasing or decreasing: 1. f() log 1 Domain: Range: Intercept(s): Asymptote(s): -values for which the function is increasing or decreasing: Chapter l Skills Practice 5

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21 Skills Practice Skills Practice for Lesson. Name Date Transformers Again! Transformations of Logarithmic Functions Problem Set Sketch and label the graph of the first function in each group. Then use that graph to sketch and label the graphs of the other two functions. 1. f() log ; f() log ; f() log 3 y f() = log f() = log f() = log 3. f() log ; f() log ( 3); f() log ( ) Chapter l Skills Practice 59

22 3. f() log ; f() log 3; f() log 1. f() In ; f() In ( 3); f() In ( ) 590 Chapter l Skills Practice

23 Name Date 5. f() In ; f() In ( 1) ; f() In ( ) 6. f() log ; f() log ( 1) 3; f() log ( ) Chapter l Skills Practice 591

24 Sketch and label the graphs of each function.. f() log and f() log ( ) 3 y f() = log( ) 1 f() = log f() log and f() log 59 Chapter l Skills Practice

25 Name Date 9. f() log ; f() log ; f() log ( ) 10. f() In ; f() In ; f() In ( ) Chapter l Skills Practice 593

26 11. f() log ; f() 1 log ( ); f() 1 log 1. f() log ; f() log ( 1 ) ; f() log ( 1 ) 59 Chapter l Skills Practice

27 Name 13. f() In ; f() In ( 1 ) ; f() In ( 1 ) Date 1. f() log ; f() log ( 3 ) ; f() log ( 3 ) Chapter l Skills Practice 595

28 15. f() log and f() log f() log and f() log( ) Chapter l Skills Practice

29 Name Date 1. f() log and f() log ( ( )) 1. f() In and f() In ( ) 3 Chapter l Skills Practice 59

30 19. f() log and f() log ( 1 3 ( 3) ) 0. f() In and f() 1 In ( ) 59 Chapter l Skills Practice

31 Name Date 1. f() log and f() log ( 1 ) 3. f() In and f() 3 In ( ) 1 Chapter l Skills Practice 599

32 600 Chapter l Skills Practice