Piecewise Defined Functions Answers

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21
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x = –4x = –2x = 0x = 2x = 4

A
x = –4
B
x = –2
C
x = 0
D
x = 2
E
x = 4
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25

Which statement is true for g(x)?

A
You can remove the discontinuity at x = 0 by defining g(0) = 0.
B
You can remove the discontinuity at x = 0 by defining g(0) = 2.
C
You can remove the discontinuity at x = 3 by defining g(3) = –1.
26

Compare and contrast the following piecewise defined functions.

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Answer:

Both functions have the same domain – all real numbers except 0. Both functions are made up of linear and quadratic pieces on their domain. Neither function is continuous; f has jump discontinuity and g has point discontinuity. The range of f is y > 1 and the range of g is all real numbers except 2.

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What is the range?

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31

Which are removable discontinuities?

A
x = –2
B
x = –2 and x = 0
C
x = 0 and x = 4
D
x = –2, x = 0, and x = 4
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What is the range?

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Option D
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A
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Option A
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Option B
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Option D
35

Which are removable discontinuities?x = –2x = –2 and x = 0✔ x = 0 and x = 4x = –2, x = 0, and x = 4

A
x = –2
B
x = –2 and x = 0
C
✔ x = 0 and x = 4
D
x = –2, x = 0, and x = 4
36

Which of the following did you include in your response?

A
Both functions have the same domain – all real numbers except 0.
B
Both functions are made up of linear and quadratic pieces on their domain.
C
Neither function is continuous; f has jump discontinuity and g has point discontinuity.
D
The range of f is y > 1 and the range of g is all real numbers except 2.

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