Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Determine the cubic function that is obtained from the parent function y = x 3 y equals , x cubed  after each sequence of transformations.

7. a vertical stretch by a factor of 3;

   a reflection across the x-axis;

   a vertical translation 2 units up;

   and a horizontal translation 1 unit right

8. a vertical stretch by a factor of 2;

   a vertical translation 4 units up;

   and a horizontal translation 3 units left

9. a reflection across the y-axis;

   a vertical translation 1 unit down;

   and a horizontal translation 5 units left

10. a vertical translation 3 units down;

    and a horizontal translation 2 units right

11. a vertical stretch by a factor of 3;

    a reflection across the y-axis;

    a vertical translation 3 4 3 fourths  unit up;

    and a horizontal translation 1 2 1 half  unit left

12. a vertical stretch by a factor of 5 3 ; 5 thirds , semicolon

    a reflection across the x-axis;

    a vertical translation 4 units down;

    and a horizontal translation 3 units right

See Problem 2.

Find all the real zeros of each function.

13. y = − 27 ( x − 2 ) 3 + 8 y equals . negative 27 . open x minus 2 close cubed . plus 8
14. y = − 1 8 ( x − 7 ) 3 − 8 y equals negative , 1 eighth . open , x minus 7 , close cubed . minus 8
15. y = − 3 ( x + 4 5 ) 3 + 8 9 y equals negative 3 . open . x plus , 4 fifths . close cubed . plus , 8 ninths
16. y = − 16 ( x + 3 ) 3 + 9 y equals . negative 16 open x plus 3 close cubed . plus 9
17. y = 4 ( x − 1 ) 3 + 10 y equals . 4 open x minus 1 close cubed . plus 10
18. y = 2 ( x + 5 ) 3 + 10 y equals . 2 open x plus 5 close cubed . plus 10

See Problem 3.

Find a quartic function with the given x-values as its only real zeros.

19. x = 2  and  x = − 1 x equals 2 , and , x equals negative 1
20. x = − 3  and  x = − 4 x equals negative 3 , and , x equals negative 4
21. x = − 1  and  x = 3 x equals negative 1 , and , x equals 3
22. x = 4  and  x = 2 x equals 4 , and , x equals 2
23. x = − 4  and  x = − 1 x equals negative 4 , and , x equals negative 1
24. x = − 3  and  x = 2 x equals negative 3 , and , x equals 2

See Problem 4.

25. Cooking The number of pepperoni slices that Kim puts on a pizza varies directly as the square of the diameter of the pizza. If she puts 15 slices on a 10 ″ 10 double prime  diameter pizza, how many slices should she put on a 16 ″ 16 double prime  diameter pizza?
26. Volume The amount of water that a spherical tank can hold varies directly as the cube of its radius. If a tank with radius 7.5 ft holds 1767  ft 3 1767 , ft cubed  of water, how much water can a tank with radius 16 ft hold?

B Apply

27. Think About a Plan The kinetic energy generated by a 5 lb ball is represented by the formula K = 1 2 ( 5 ) v 2 . k equals , 1 half . open 5 close . v squared . .  If the ball is thrown with a velocity of 6 ft/sec, how much kinetic energy is generated?

    • What does 5 represent in the function?
    • What number should you substitute for v?

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