Applying Absolute Functions in Real-World Scenarios

A hiker is climbing a mountain. The height of the mountain above sea level can be modeled by the function h(x) = |x - 3000| + 2000, where x is the distance in meters from the base of the mountain. How high is the mountain when the hiker is 4000 meters from the base?

• 2500 meters

• 3500 meters

• 4000 meters

• 3000 meters

A delivery truck's distance from a warehouse can be modeled by the function d(t) = |t - 50| + 20, where t is the time in minutes since leaving the warehouse. How far is the truck from the warehouse after 30 minutes?

• 40

• 60

• 30

• 50

The temperature in a city can be modeled by the function T(x) = |x - 15| + 10, where x is the number of hours since midnight. What is the temperature at 10 AM?

• 20

• 15

• 5

• 25

A car's speed can be modeled by the function s(t) = |t - 60| + 40, where t is the speed limit in km/h. If the speed limit is 80 km/h, what is the car's speed?

• 40 km/h

• 80 km/h

• 60 km/h

• 100 km/h

A company's profit can be modeled by the function P(x) = |x - 100| + 500, where x is the number of units sold. What is the profit when 120 units are sold?

• 500

• 520

• 600

• 550

A person's height above sea level can be modeled by the function h(d) = |d - 500| + 100, where d is the distance in meters from sea level. How high is the person when they are 600 meters above sea level?

• 400 meters

• 100 meters

• 300 meters

• 200 meters

The cost of a taxi ride can be modeled by the function C(m) = |m - 10| + 15, where m is the distance in miles. What is the cost for a 12-mile ride?

• 20

• 17

• 25

• 10

A basketball player's score can be modeled by the function S(x) = |x - 20| + 30, where x is the number of points scored. How many points does the player score if they scored 25 points?

• 40

• 25

• 35

• 30

A factory's production can be modeled by the function P(x) = |x - 200| + 1000, where x is the number of items produced. What is the production level when 250 items are produced?

• 950

• 1050

• 1100

• 1200

A swimmer's distance from the shore can be modeled by the function d(t) = |t - 15| + 5, where t is the time in minutes. How far is the swimmer from the shore after 10 minutes?

• 15

• 10

• 5

• 20