Name Date. Work with a partner. Each graph shown is a transformation of the parent function

Transcription

1 3. Transformations of Eponential and Logarithmic Functions For use with Eploration 3. Essential Question How can ou transform the graphs of eponential and logarithmic functions? 1 EXPLORATION: Identifing Transformations Work with a partner. Each graph shown is a transformation of the parent function e or f ln. f Match each function with its graph. Eplain our reasoning. Then describe the transformation of f represented b g. a. g e + 3 b. g e c. g e 1 d. g ln( + ) e. g + ln f. g + ln( ) A. B. C. D. E. F. 111 Copright Big Ideas Learning, LLC

2 _ 3. Transformations of Eponential and Logarithmic Functions (continued) EXPLORATION: Characteristics of Graphs Work with a partner. Determine the domain, range, and asmptote of each function in Eploration 1. Justif our answers. Communicate Your Answer 3. How can ou transform the graphs of eponential and logarithmic functions?. Find the inverse of each function in Eploration 1. Then check our answer b using a graphing calculator to graph each function and its inverse in the same viewing window. Copright Big Ideas Learning, LLC 11

3 3. Notetaking with Vocabular For use after Lesson 3. In our own words, write the meaning of each vocabular term. eponential function logarithmic function transformations Core Concepts Transformation f Notation Eamples Horizontal Translation Graph shifts left or right. f ( h) Vertical Translation Graph shifts up or down. f Reflection Graph flips over - or -ais. f + f k g g g g g g 3 3 units right + units left units up 1 1 unit down in the -ais in the -ais Horizontal Stretch or Shrink Graph stretches awa from or shrinks toward -ais Vertical Stretch or Shrink Graph stretches awa from or shrinks toward -ais f ( a ) a f g g ( ) ( ) g g shrink b a factor of 1 stretch b a factor of 3 stretch b a factor of 3 1 shrink b a factor of 1 Notes: 113 Copright Big Ideas Learning, LLC

4 _ 3. Notetaking with Vocabular (continued) Transformation f( ) Notation Eamples Horizontal Translation Graph shifts left or right. f ( h ) ( ) ( + ) g g log units right log 7 7 units left Vertical Translation Graph shifts up or down. f Reflection Graph flips over - or -ais. f + ( ) f k g g log units up log 1 1 unit down log( ) log g in the -ais g in the -ais Horizontal Stretch or Shrink Graph stretches awa from or shrinks toward -ais Vertical Stretch or Shrink Graph stretches awa from or shrinks toward -ais f ( a ) a f log g 1 g shrink b a factor of 1 log stretch b a factor of log stretch b a factor of 5 log shrink b a factor of g g 3 3 Notes: Copright Big Ideas Learning, LLC 11

5 3. Notetaking with Vocabular (continued) Practice A Etra Practice In Eercises 1 6, describe the transformation of f represented b g. Then graph each function. 1. f 6, g f e, g e 3. f log, g 1 log ( + 7). 5 5 f log, g log f, g f log, g 3 log( ) 115 Copright Big Ideas Learning, LLC

6 Practice 5.3 BPractice B In Eercises 1 8, describe the transformation of f represented b g. Then graph each function f e, g e. f, g( ). f( 1 ) g 1 f e, g e 5 3., f 3, g f e, g e + 8. f( 1 ) g 1 f e, g e Describe and correct the error in graphing the function, f. 1 8 (0, ) (1, 5) (, 7) In Eercises 10 and 11, describe the transformation of f represented b g. Then graph each function. 10. f log, g log ( ) f log, g log ( ) In Eercises 1 1, write a rule for g that represents the indicated transformation of the graph of f. 1. f 5 ; reflection in the -ais, followed b a horizontal shrink b a factor of and a translation units down 13. f e ; translation units left and 3 units up, followed b a vertical stretch b a factor of f log ; translation 5 units right and units down, followed b a reflection in the -ais 1. 1 Copright Big Ideas Learning, LLC 116