Chap 2 Section6

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 2.6 Horizontal Geometric Transformations 209 Version: Fall 2007 2.6 Exercises Pictured below is the graph of a function f . x 10 y 10 f The table that follows evaluates the function f in the plot at key values of x . Notice the horizontal format, where the first point in the table is the ordered pair ( 6 , 0) . x 6 4 2 0 2 4 f ( x ) 0 4 4 0 2 0 Use the graph and the table to complete each of following tasks for Exercises 1 - 10 . i. Set up a coordinate system on graph paper. Label and scale each axis, then copy and label the original graph of f onto your coordinate system. Re- member to draw all lines with a ruler. ii. Use the original table to help com- plete the table for the given function in the exercise. iii. Using a different colored pencil, plot the data from your completed table on the same coordinate system as the original graph of f . Use these points Copyrighted material. See: 1 to help complete the graph of the given function in the exercise, then label this graph with its equation given in the exercise. 1. y = f (2 x ) . x 3 2 1 0 1 2 y 2. y = f ((1 / 2) x ) . x 12 8 4 0 4 8 y 3. y = f ( x ) . x 4 2 0 2 4 6 y 4. y = f ( x + 3) . x 9 7 5 3 1 1 y 5. y = f ( x 1) . x 5 3 1 1 3 5 y 6. y = f ( 2 x ) . x 2 1 0 1 2 3 y
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210 Chapter 2 Functions Version: Fall 2007 7. y = f (( 1 / 2) x ) . x 8 4 0 4 8 12 y 8. y = f ( x 2) . x 6 4 2 0 2 4 y 9. y = f ( x + 1) . x 3 1 1 3 5 7 y 10. y = f ( x/ 4) . x 16 8 0 8 16 24 y 11. Use your graphing calculator to draw the graph of y = x . Then, draw the graph of y = x . In your own words, explain what you learned from this exer- cise. 12. Use your graphing calculator to draw the graph of y = | x | . Then, draw the graph of y = | − x | . In your own words, explain what you learned from this exer- cise. 13. Use your graphing calculator to draw the graph of y = x 2 . Then, in succession, draw the graphs of y = ( x 2) 2 , y = ( x 4) 2 , and y = ( x 6) 2 . In your own words, explain what you learned from this exercise. 14. Use your graphing calculator to draw the graph of y = x 2 . Then, in succession, draw the graphs of y = ( x + 2) 2 , y = ( x + 4) 2 , and y = ( x + 6) 2 . In your own words, explain what you learned from this exercise. 15. Use your graphing calculator to draw the graph of y = | x | . Then, in succession, draw the graphs of y = | 2 x | , y = | 3 x | , and y = | 4 x | . In your own words, explain what you learned from this exercise. 16. Use your graphing calculator to draw the graph of y = | x | . Then, in succession, draw the graphs of y = | (1 / 2) x | , y = | (1 / 3) x | , and y = | (1 / 4) x | . In your own words, explain what you learned from this exercise.
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