Inequalities & Piecewise Functions: Word Problem Challenge

1. A temperature range is given as |T - 20| < 5. What are the possible values for T?

• 10 < T < 20

• 20 < T < 30

• 15 < T < 25

• T < 15 or T > 25

2. A store sells a jacket for $80. If the price is discounted by an absolute value of at most $15, what is the range of possible prices?

• $50 to $65

• $65 to $80

• $60 to $75

• $70 to $85

3. The height of a plant is modeled by the piecewise function: h(t) = { 2t + 1 for t < 3, 5 for t = 3, 3t - 2 for t > 3 }. What is the height of the plant at t = 4?

• 10

• 12

• 8

• 6

4. A car's speed is limited by the inequality |s - 60| ≤ 10. What is the range of speeds allowed for the car?

• 55 to 65

• 40 to 80

• 30 to 90

• The range of speeds allowed for the car is 50 to 70.

5. A piecewise function defines the cost of a taxi ride: C(d) = { 5 for d ≤ 1, 5 + 2(d - 1) for 1 < d ≤ 5, 15 for d > 5 }. What is the cost for a 3-mile ride?

• 12

• 9

• 20

• 7

6. The absolute value inequality |x + 3| > 7 represents what range of values for x?

• -10 < x < 4

• x < -7 or x > 0

• x < -10 or x > 4

• x > -3 and x < 4

7. A swimming pool's water level is maintained within 2 feet of a target level of 10 feet. Write the absolute value inequality that represents this situation and solve for the range of acceptable water levels.

• 7 ≤ x ≤ 11

• 9 ≤ x ≤ 13

• 6 ≤ x ≤ 10

• 8 ≤ x ≤ 12

8. A piecewise function describes the shipping cost: S(w) = { 10 for w ≤ 5, 10 + 1.5(w - 5) for 5 < w ≤ 20, 40 for w > 20 }. What is the shipping cost for a package weighing 15 pounds?

• 30

• 15

• 50

• 25

9. The inequality |x - 4| < 3 can be solved to find the range of x. What is that range?

• (4, 10)

• (1, 7)

• (3, 5)

• (0, 4)

10. A delivery service charges based on distance traveled: D(d) = { 5 for d ≤ 2, 5 + 3(d - 2) for d > 2 }. What is the cost for a delivery of 4 miles?

• 11

• 15

• 20

• 8