Practice and Problem-Solving Exercises

A Practice

How is each function related to y = x? Graph the function by translating the parent function. See Problem 1.

10. y = x − 3 y equals x minus 3
11. y = x + 4.5 y equals x plus 4.5
12. y = x + 1.5 y equals x plus 1.5

Make a table of values for f(x) after the given translation.

13. 3 units up

    x	f(x)
    − 2 negative 2	3
    0	1
    1	− 2 negative 2
    3	− 1 negative 1

14. 1 unit down

    x	f(x)
    − 1 negative 1	1
    0	0
    2	− 4 negative 4
    3	2

15. 4 units up

    x	f(x)
    − 3 negative 3	1
    − 1 negative 1	− 2 negative 2
    1	0
    4	3

Write an equation for each vertical translation of y = f(x).

16. 2 3 2 thirds  unit down
17. 4 units up
18. 2 units up

For each function, identify the horizontal translation of the parent function, f ( x ) = x 2 . f open x close equals , x squared , .  Then graph the function. See Problems 2 and 3.

19. y = ( x − 4 ) 2 y equals . open x minus 4 close squared
20. y = ( x + 1 ) 2 y equals . open x plus 1 close squared
21. y = ( x + 3 ) 2 y equals . open x plus 3 close squared

22. The graph of the function f(x) is shown below.

    

    1. Make a table of values for f(x) and f ( x + 3 ) . f open x plus 3 close .
    2. Graph f(x) and f ( x + 3 ) open x plus 3 close  on the same coordinate grid.

Write the function rule for each function reflected in the given axis.

23. f ( x ) = x + 1 ; x -axis f open x close equals x plus 1 semicolon x , minusaxis
24. f ( x ) = 3 x ; y -axis f open x close equals 3 x semicolon y , minusaxis
25. f ( x ) = 2 x − 4 ; x -axis f open x close equals 2 x minus 4 semicolon x , minusaxis

Write an equation for each transformation of y = x. See Problem 4.

26. vertical stretch by a factor of 4
27. vertical stretch by a factor of 2
28. vertical compression by a factor of 1 2 1 half
29. vertical compression by a factor of 1 4 1 fourth

Write the function rule g(x) after the given transformations of the graph of f ( x ) = 4 x . f open x close equals 4 x .  See Problem 5.

30. translation up 5 units; reflection in the x-axis
31. reflection in the y-axis; vertical compression by a factor of 1 8 1 eighth

Describe the transformations of f(x) that produce g(x).

32. f ( x ) = x 2 ; g ( x ) = − 2 x + 4 f open x close equals , x over 2 , semicolon g open x close equals negative 2 x plus 4
33. f ( x ) = 3 x ; g ( x ) = ( 3 x 4 − 2 ) f , open x close , equals 3 x semicolon g , open x close , equals . open . fraction 3 x , over 4 end fraction , minus 2 . close

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