Chap2 Section5

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

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Section 2.5 Vertical Geometric Transformations 183 Version: Fall 2007 2.5 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 ( 4 , 0) . x 4 3 0 2 5 6 f ( x ) 0 4 4 4 4 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 = 2 f ( x ) . x 4 3 0 2 5 6 y 2. y = (1 / 2) f ( x ) . x 4 3 0 2 5 6 y 3. y = f ( x ) . x 4 3 0 2 5 6 y 4. y = f ( x ) 2 . x 4 3 0 2 5 6 y 5. y = f ( x ) + 4 . x 4 3 0 2 5 6 y 6. y = 2 f ( x ) . x 4 3 0 2 5 6 y
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184 Chapter 2 Functions Version: Fall 2007 7. y = ( 1 / 2) f ( x ) . x 4 3 0 2 5 6 y 8. y = f ( x ) + 3 . x 4 3 0 2 5 6 y 9. y = f ( x ) 2 . x 4 3 0 2 5 6 y 10. y = ( 1 / 2) f ( x ) + 3 . x 4 3 0 2 5 6 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 2 4 , and y = x 2 6 . In your own words, ex- plain what you learned from this exer- cise. 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 2 +4 , and y = x 2 + 6 . In your own words, ex- plain what you learned from this exer- cise. 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. Pictured below is the graph of a function f . In Exercises 17 - 22 , use this graph to perform each of the following tasks. x 10 y 10 f i. Set up a coordinate system on a sheet of graph paper. Label and scale each axis. Make an exact copy of the graph of f on your coordinate system. Re- member to draw all lines with a ruler.
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