# CEOE Advanced Math: Piecewise, Absolute Value & Step Functions Chapter Exam

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### Page 1

#### Question 1 1. If f(x) represents the left part of the black graph and g(x) represents the right part of the black graph, then what piecewise function represents the red graph?

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Question 2
2.
Evaluate the following piecewise function for x = 2 and x = -7.

f(x) = 2x + 3, x ≤ -5

f(x) = x³, x > -5

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Question 3
3.
Which portion(s) of this piecewise function would include an open endpoint?

f(x) = 2x +3, x>2

f(x) = 3x - 4, x = 2

f(x) = x-2, x <2

#### Question 4 4. Which of the following is NOT a piecewise function?

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Question 5
5.
The graph displayed is a graph of a step function *P*. Evaluate *P*(-2.4), *P*(1), and *P*(3.47).

### Page 2

#### Question 6 6. What is the domain of this function?

#### Question 7 7. What translations have been made to f(x)?

#### Question 8 8. What is the domain of this function?

#### Question 9 9. In which function has f(x) been shifted up 2 units and 7 units to the right?

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Question 10
10.
You have a summer job that pays time and a half for overtime (any hours over 40 in a week). Overtime is 1.5 times your hourly rate of $7.00/hr.

How much money will you make if you work 50 hours in one week?

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#### Question 11 11. What is the domain of a piecewise function?

#### Question 12 12. What is the most common piecewise function?

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Question 13
13.
Evaluate the following piecewise function for x = 0 and x = 5.

f(x) = 2x - 3, x < 0

f(x) = x² - 1, x = 0

f(x) = x + 3, x > 0

#### Question 14 14. Take the following function, shift it up 1 unit, and reflect it about the x-axis:

#### Question 15 15. The set of input, or x, values for which the function is defined is called the _____.

### Page 4

#### Question 16 16. If a step function contains the right most (the largest endpoint) endpoint and not the left most endpoint (the smallest endpoint) of each interval, then is it a variation of the floor function or the ceiling function?

#### Question 17 17. What is the term for a function whose graph looks like a series of steps?

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Question 18
18.
Your cell phone plan costs $75/month and gives you unlimited talking time and 500 text messages per month. After 500 text messages, it costs $0.10 per text you send.

If you send 870 texts in January, how much is your total cell phone bill?

#### Question 19 19. Which piecewise function is represented by this graph?

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Question 20
20.
Which graph represents this piecewise function?

f(x) = 2x, x < 1

f(x) = x² - 1, x ≥ 1

### Page 5

#### Question 21 21. All of the following are piecewise functions, EXCEPT:

#### Question 22 22. Evaluate the following for the greatest and least integer function.

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Question 23
23.
If *H* represents the heaviside function, then what is *H*(7.7), *H*(-1), and *H*(0)?

#### Question 24 24. What is the domain of this function?

#### Question 25 25. What translations have been made to g(x)?

#### CEOE Advanced Math: Piecewise, Absolute Value & Step Functions Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!