Evaluating Absolute Values and Piecewise Functions

1. A temperature is recorded as -5 degrees Celsius. If the temperature rises by an absolute value of x degrees, what is the range of possible temperatures? Solve the inequality |x| < 10.

• [-15, 5]

• [-5, 15]

• [-10, 10]

• [-20, 0]

2. A piecewise function f(x) is defined as follows: f(x) = { 2x + 3, if x < 0; 5, if 0 ≤ x ≤ 2; x^2, if x > 2 }. What is f(-2)?

• 4

• 0

• 1

• -1

3. A car's speed is represented by the absolute value inequality |s - 60| ≤ 10, where s is the speed in miles per hour. What is the range of speeds the car can travel?

• 40 ≤ s ≤ 60

• 30 ≤ s ≤ 50

• 60 ≤ s ≤ 80

• 50 ≤ s ≤ 70

4. Evaluate the piecewise function g(x) = { x + 4, if x < 1; 3x - 1, if 1 ≤ x < 3; 2, if x ≥ 3 } at x = 2.

• 5

• 4

• 7

• 6

5. A store has a sale where the price of an item is given by the piecewise function p(x) = { 50, if x < 5; 40, if 5 ≤ x < 10; 30, if x ≥ 10 }. What is the price if you buy 7 items?

• 250

• 280

• 300

• 350

6. Solve the absolute value inequality |3x - 12| > 6 and interpret the solution in the context of a distance problem.

• x < 2 or x > 6

• x < 0 or x > 8

• 2 < x < 6

• x = 4

7. For the piecewise function h(x) = { x^2, if x < 0; 2x + 1, if 0 ≤ x < 4; 10, if x ≥ 4 }, find h(5).

• 10

• 5

• 8

• 12

8. A runner's distance from the starting point is modeled by the inequality |d - 100| ≤ 20, where d is the distance in meters. What are the possible distances the runner can be from the starting point?

• 80 ≤ d ≤ 120

• 100 ≤ d ≤ 140

• 60 ≤ d ≤ 100

• 80 ≤ d ≤ 90

9. Evaluate the piecewise function k(x) = { 3x - 2, if x < 2; 4, if x = 2; x/2, if x > 2 } at x = 2 and x = 3.

• k(2) = 3, k(3) = 2

• k(2) = 4, k(3) = 2

• k(2) = 4, k(3) = 1.5

• k(2) = 5, k(3) = 0

10. A delivery service charges based on distance using the piecewise function c(d) = { 5, if d < 1; 10, if 1 ≤ d < 5; 20, if d ≥ 5 }. How much would it cost to deliver a package 3 miles away?

• 25

• 15

• 5

• 10