Piecewise, Operations, & Compositions Test Review

Identify the domain of the piecewise graph below.

• (-∞, ∞)

• (-∞, 2) ∪ (2, ∞)

• (-∞, 6)

• (-∞, 0) ∪ (0, 6]

Identify the range of the piecewise graph below.

• (-∞, ∞)

• (-∞, 2) ∪ (2, ∞)

• (-∞, 6]

• (-∞, 6)

• (-∞, ∞)

• (-∞, 4) ∪ (4, ∞)

• (1, ∞)

• [1, ∞)

• (-∞, ∞)

• (-∞, 4) ∪ (4, ∞)

• (1, ∞)

• [1, ∞)

Which of the following piecewise functions represents the graph below?

• f(x) = -3x + 5, x < 1

  -6, x = 1

  2, 1 < x < 6

• f(x) = -3x + 5, x ≤ 1

  -6, x = 1

  2, 1 < x < 6

• f(x) = -3x + 5, x ≤ 1

  -6, x = 1

  2, 1 ≤ x < 6

• f(x) = -3x + 5, x < 1

  -6, x ≠ 1

  2, 1 < x < 6

You have a summer job that pays time and a half for overtime (for anything over 40 hours). After that you earn 1.5 times your hourly rate of $10.00 per hour. Write a piecewise function that models this situation.

• 10.00x, x ≤ 40

  400 + 15.00(x-40), x > 40

• f10.00x, x < 40

  400 + 15.00(x-40), x ≥ 40

• 10.00x, x < 40

  15.00(x - 40), x ≥ 40

• 10.00x, x ≤ 40

  15.00(x - 40), x > 40

A lawyer’s fee is based on length of time. If she sees a client for up to 30 minutes, she charges $200. She charges $250 for anything over 30 minutes up to 45 minutes. If she sees a client for more than 45 minutes, she charges $250 plus $5 per minute for each minute above 45 minutes. Write a piecewise function to model this situation.

• 200 for x ≤ 30

  250 for 30 < x ≤ 45

  250 + 5(x - 45) for x > 45

• 200 for x < 30

  250 for 30 < x ≤ 45

  250 + 5(x - 45) for x > 45

• 200 for x ≤ 30

  250 for 30 < x < 45

  250 + 5(x - 45) for x ≥ 45

• 200 for x < 30

  250 for 30 < x < 45

  250 + 5(x - 45) for x ≥ 45

What is the value of f(1) - g(-2) based on the given graphs?

• -4

• 2

• 0

• 5

Evaluate f(-3) - g(0) using the provided graphs.

• -6

• -3

• 8

• 0

What is the value of 3f(-2) + g(2) based on the graphs?

• -1

• -11

• 9

• -30