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8.8E: Exercises

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Practice Makes Perfect

Exercise 8.8E.17 Evaluate a Radical Function

In the following exercises, evaluate each function.

  1. f(x)=4x4, find
    1. f(5)
    2. f(0)
  2. f(x)=6x5, find
    1. f(5)
    2. f(1)
  3. g(x)=6x+1, find
    1. g(4)
    2. g(8)
  4. g(x)=3x+1, find
    1. g(8)
    2. g(5)
  5. F(x)=32x, find
    1. F(1)
    2. F(11)
  6. F(x)=84x, find
    1. F(1)
    2. F(2)
  7. G(x)=5x1, find
    1. G(5)
    2. G(2)
  8. G(x)=4x+1, find
    1. G(11)
    2. G(2)
  9. g(x)=32x4, find
    1. g(6)
    2. g(2)
  10. g(x)=37x1, find
    1. g(4)
    2. g(1)
  11. h(x)=3x24, find
    1. h(2)
    2. h(6)
  12. h(x)=3x2+4, find
    1. h(2)
    2. h(6)
  13. For the function f(x)=42x3, find
    1. f(0)
    2. f(2)
  14. For the function f(x)=43x3, find
    1. f(0)
    2. f(3)
  15. For the function g(x)=444x, find
    1. g(1)
    2. g(3)
  16. For the function g(x)=484x, find
    1. g(6)
    2. g(2)
Answer

1.

  1. f(5)=4
  2. no value at x=0

3.

  1. g(4)=5
  2. g(8)=7

5.

  1. F(1)=1
  2. F(11)=5

7.

  1. G(5)=26
  2. G(2)=3

9.

  1. g(6)=2
  2. g(2)=2

11.

  1. h(2)=0
  2. h(6)=234

13.

  1. f(0)=0
  2. f(2)=2

15.

  1. g(1)=0
  2. g(3)=2
Exercise 8.8E.18 Find the Domain of a Radical Function

In the following exercises, find the domain of the function and write the domain in interval notation.

  1. f(x)=3x1
  2. f(x)=4x2
  3. g(x)=23x
  4. g(x)=8x
  5. h(x)=5x2
  6. h(x)=6x+3
  7. f(x)=x+3x2
  8. f(x)=x1x+4
  9. g(x)=38x1
  10. g(x)=36x+5
  11. f(x)=34x216
  12. f(x)=36x225
  13. F(x)=48x+3
  14. F(x)=4107x
  15. G(x)=52x1
  16. G(x)=56x3
Answer

1. [13,)

3. (,23]

5. (2,)

7. (,3](2,)

9. (,)

11. (,)

13. [38,)

15. (,)

Exercise 8.8E.19 graph radical functions

In the following exercises,

  1. find the domain of the function
  2. graph the function
  3. use the graph to determine the range
    1. f(x)=x+1
    2. f(x)=x1
    3. g(x)=x+4
    4. g(x)=x4
    5. f(x)=x+2
    6. f(x)=x2
    7. g(x)=2x
    8. g(x)=3x
    9. f(x)=3x
    10. f(x)=4x
    11. g(x)=x
    12. g(x)=x+1
    13. f(x)=3x+1
    14. f(x)=3x1
    15. g(x)=3x+2
    16. g(x)=3x2
    17. f(x)=3x+3
    18. f(x)=3x3
    19. g(x)=3x
    20. g(x)=3x
    21. f(x)=23x
    22. f(x)=23x
Answer

1.

  1. domain: [1,)

  2. The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 1 to 7. The y-axis runs from negative 2 to 10. The function has a starting point at (negative 1, 0) and goes through the points (0, 1) and (3, 2).
    Figure 8.7.8
  3. [0,)

3.

  1. domain: [4,)

  2. The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a starting point at (negative 4, 0) and goes through the points (negative 3, 1) and (0, 2).
    Figure 8.7.9
  3. [0,)

5.

  1. domain: [0,)

  2. The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 2) and goes through the points (1, 3) and (4, 4).
    Figure 8.7.10
  3. [2,)

7.

  1. domain: [0,)

  2. The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from 0 to 8. The function has a starting point at (0, 0) and goes through the points (1, 2) and (4, 4).
    Figure 8.7.11
  3. [0,)

9.

  1. domain: (,3]

  2. The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 6 to 4. The y-axis runs from 0 to 8. The function has a starting point at (3, 0) and goes through the points (2, 1), (negative 1, 2), and (negative 6, 3).
    Figure 8.7.12
  3. [0,)

11.

  1. domain: [0,)

  2. The figure shows a square root function graph on the x y-coordinate plane. The x-axis of the plane runs from 0 to 8. The y-axis runs from negative 8 to 0. The function has a starting point at (0, 0) and goes through the points (1, negative 1) and (4, negative 2).
    Figure 8.7.13
  3. (,0]

13.

  1. domain: (,)

  2. The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 1, 0) and goes through the points (negative 2, negative 1) and (0, 1).
    Figure 8.7.14
  3. (,)

15.

  1. domain: (,)

  2. The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (negative 4, 0) and goes through the points (negative 3, negative 1) and (negative 1, 1).
    Figure 8.7.15
  3. (,)

17.

  1. domain: (,)

  2. The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 2 to 6. The function has a center point at (0, 3) and goes through the points (negative 1, 2) and (1, 4).
    Figure 8.7.16
  3. (,)

19.

  1. domain: (,)

  2. The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 1) and (negative 1, negative 1).
    Figure 8.7.17
  3. (,)

21.

  1. domain: (,)

  2. The figure shows a cube root function graph on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis runs from negative 4 to 4. The function has a center point at (0, 0) and goes through the points (1, 2) and (negative 1, negative 2).
    Figure 8.7.18
  3. (,)
Exercise 8.8E.20 writing exercises
  1. Explain how to find the domain of a fourth root function.
  2. Explain how to find the domain of a fifth root function.
  3. Explain why y=3x is a function.
  4. Explain why the process of finding the domain of a radical function with an even index is different from the process when the index is odd.
Answer

1. Answers may vary

3. Answers may vary

Self Check

a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

The table has 4 columns and 4 rows. The first row is a header row with the headers “I can…”, “Confidently”, “With some help.”, and “No – I don’t get it!”. The first column contains the phrases “evaluate a radical function”, “find the domain of a radical function”, and “graph a radical function”. The other columns are left blank so the learner can indicate their level of understanding.
Figure 8.7.19

b. What does this checklist tell you about your mastery of this section? What steps will you take to improve?


This page titled 8.8E: Exercises is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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