Interpreting Absolute Value Functions in Real Life

1. A temperature sensor records the temperature in degrees Celsius. If the temperature is represented by the function T(x) = |x - 20|, where x is the actual temperature, what does T(15) represent in this context?

• 5 degrees Celsius

• 10 degrees Celsius

• 0 degrees Celsius

• 15 degrees Celsius

2. A diver is 10 meters below sea level. The depth of the diver can be modeled by the function D(x) = |x|, where x is the depth in meters. What is the diver's depth when x = -10?

• 5 meters

• 15 meters

• 0 meters

• 10 meters

3. A car's distance from a checkpoint can be modeled by the function D(t) = |t - 50|, where t is the time in minutes. What does D(60) represent?

• 40

• 30

• 20

• 10

4. The height of a ball thrown into the air can be modeled by the function H(t) = -|t - 5| + 20. What is the maximum height of the ball?

• 25

• 15

• 20

• 10

5. A company's profit can be modeled by the function P(x) = |x - 100|, where x is the number of units sold. What does P(120) indicate about the company's profit?

• The company's profit when selling 120 units is 0.

• The company's profit when selling 120 units is 20.

• The company's profit when selling 120 units is 50.

• The company's profit when selling 120 units is 100.

6. A mountain's elevation can be represented by the function E(x) = |x|, where x is the distance from the base in kilometers. What is the elevation at x = 3 km?

• 2 km

• 5 km

• 3 km

• 0 km

7. A person walks away from a starting point, and their distance from the starting point can be modeled by the function D(t) = |t - 10|, where t is the time in minutes. What does D(5) represent?

• 10

• 0

• 5

• 15

8. The distance of a point from the origin in a coordinate plane can be modeled by the function D(x, y) = |x| + |y|. What is the distance from the origin for the point (3, -4)?

• 9

• 12

• 7

• 5

9. A store's revenue can be modeled by the function R(x) = |x - 200|, where x is the number of items sold. What does R(250) tell us about the store's revenue?

• The store's revenue when 250 items are sold is 100.

• The store's revenue when 250 items are sold is 200.

• The store's revenue when 250 items are sold is 0.

• The store's revenue when 250 items are sold is 50.

10. A roller coaster's height above ground can be modeled by the function H(x) = |x - 15|, where x is the distance from the starting point in meters. What is the height when x = 20 meters?

• 10 meters

• 0 meters

• 5 meters

• 15 meters