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4.3E: Exercises - Understanding Transformations of Functions

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Exercise 4.3E.1

Match the graph to the function definition.

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Figure 2.5.18
2fe54b1c80ea84f0f721462f90455c0b.png
Figure 2.5.19
3622a0d2256166544a122ecd7156de36.png
Figure 2.5.20
47088a9efd6814511cb0fc8d233b539f.png
Figure 2.5.21
d44d62205d34ed371aad179b77c54a81.png
Figure 2.5.22
Figure 2.5.23
  1. f(x)=x+4
  2. f(x)=|x2|2
  3. f(x)=x+11
  4. f(x)=|x2|+1
  5. f(x)=x+4+1
  6. f(x)=|x+2|2
Answer

1. e

3. d

5. f

Exercise 4.3E.2

Graph the given function. Identify the basic function and translations used to sketch the graph. Then state the domain and range.

  1. g(x)=4
  2. g(x)=2
  3. f(x)=x+3
  4. f(x)=x2
  5. g(x)=x2+1
  6. g(x)=x24
  7. g(x)=(x5)2+2
  8. g(x)=(x+2)25
  9. h(x)=|x1|3
  10. h(x)=|x+2|5
  11. g(x)=x2+1
  12. g(x)=x+2+3
  13. h(x)=(x1)34
  14. h(x)=(x+1)3+3
  15. f(x)=1x+12
  16. f(x)=1x3+3
  17. f(x)=3x2+6
  18. f(x)=3x+84
Answer

1. Basic graph y=4; domain: (,); range: {4}

dec428893d68980da985eabaf7f7fb11.png
Figure 2.5.37

3. y=x; Shift up 3 units; domain: (,); range: (,)

ed14f13811bfb7c397b768ab1e6d718a.png
Figure 2.5.24

5. y=x2; Shift up 1 unit; domain: (,); range: [1,)

0e393f0d6e151259a123b1e505dec86b.png
Figure 2.5.25

7. y=x2; Shift right 5 units and up 2 units; domain: (,); range: [2,)

57a5fd7bcf0e225b10961c6534cd4545.png
Figure 2.5.27

9. y=|x|; Shift right 1 unit and down 3 units; domain: (,); range: [3,)

424b66df0df22a96fd88c4957413d44e.png
Figure 2.5.29

11. y=x; Shift right 2 units and up 1 unit; domain: [2,); range: [1,)

da6d3f21b303aeb0b29fe4975b48a64f.png
Figure 2.5.31

13. y=x3; Shift right 1 unit and down 4 units; domain: (,); range: (,)

a4f584febcd95dc5ef92bbe2ef80df7c.png
Figure 2.5.33

15. y=1x; Shift left 1 unit and down 2 units; domain: (,1)(1,); range: (,2)(2,)

0eac4ad67881e57bfa8e7dc46c933e8e.png
Figure 2.5.36

17. y=3x; Shift up 6 units and right 2 units; domain: (,); range: (,)

43dafc2ae310a7b8dbba8ee467325ad8.png
Figure 2.5.38

Exercise 4.3E.3

Graph the piecewise functions.

  1. h(x)={x2+2 if x<0x+2 if x0
  2. h(x)={x23 if x<0x3 if x0
  3. h(x)={x31 if x<0|x3|4 if x0
  4. h(x)={x3 if x<0(x1)21 if x0
Answer

1.

1790a36f5e4c391f1d37b3abdabb2349.png
Figure 2.5.39

3.

f2e8945e9fea8dc040b6d5a1180fd1d0.png
Figure 2.5.40

Exercise 4.3E.4

Write an equation that represents the function whose graph is given.

1.

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Figure 2.5.43

2.

122abd4ccb8eb72a59532b22ed6116ab.png
Figure 2.5.44

3.

b8f5c01476fe7ee9f21dd781da420d2d.png
Figure 2.5.45

4.

Figure 2.5.46

5.

e90ad3255312e9bf25d0f866de703eb4.png
Figure 2.5.47

6.

6c160b69a9ef56763a5424ea14fbc86f.png
Figure 2.5.48

7.

613f12af91bfbf853201387cb6dd7acb.png
Figure 2.5.49

8.

Figure 2.5.50
Answer

1. f(x)=x5

3. f(x)=(x15)210

5. f(x)=1x+8+4

7. f(x)=x+164

Exercise 4.3E.5

Match the graph to the given function definition.

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Figure 2.5.51
7ddabfc77a72214e9f6bea00e3b2cca0.png
Figure 2.5.52
039e6f4a86d07a578660882bccf7ea40.png
Figure 2.5.53
16b19343fd01aecf51c1cdea8af3ee21.png
Figure 2.5.54
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Figure 2.5.55
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Figure 2.5.56
  1. f(x)=3|x|
  2. f(x)=(x+3)21
  3. f(x)=|x+1|+2
  4. f(x)=x2+1
  5. f(x)=13|x|
  6. f(x)=(x2)2+2
Answer

1. b

3. d

5. f

Exercise 4.3E.6

Use the transformations to graph the following functions.

  1. f(x)=x+5
  2. f(x)=|x|3
  3. g(x)=|x1|
  4. f(x)=(x+2)2
  5. h(x)=x+2
  6. h(x)=x2+1
  7. g(x)=x3+4
  8. f(x)=x2+6
Answer

1.

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Figure 2.5.57

3.

8e5290466d22bfaad7a33f4ffcc1c2d0.png
Figure 2.5.58

5.

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Figure 2.5.59

7.

92bf8584935a01fd897e3af4c08fa4fd.png
Figure 2.5.61

4.3E: Exercises - Understanding Transformations of Functions is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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