MathIsimple

Function Applications

Learn to model real-world scenarios with functions, calculate rates of change, analyze domain and range, and solve applied problems using function concepts!

10th Grade
Functions
~60 min
🎮 Interactive Activity: Function Modeler

Model the real-world scenario with a function!

Scenario:

A car travels at 60 mph. Distance after t hours?
🎮 Interactive Activity: Rate of Change Calculator

Calculate the average rate of change!

Function:

f(x) = 3x + 5

From x = 1 to x = 4

1. Introduction to Function Applications

Why Functions Matter

Functions are powerful tools for modeling real-world relationships. They help us understand how one quantity depends on another.

Common Function Types in Applications:

  • Linear: Constant rate of change (distance, cost per unit)
  • Quadratic: Projectile motion, area problems, optimization
  • Exponential: Population growth, compound interest, decay
  • Polynomial: Volume, complex relationships
Example 1: Linear Model

A taxi charges $3 base fare plus $2 per mile. Write a function for total cost.

Variables: x = miles, C = total cost

Function: C(x) = 2x + 3

Interpretation: $2 per mile (slope) + $3 base (y-intercept)

Example 2: Quadratic Model

A ball is thrown from 5 feet high with initial velocity 32 ft/s upward.

Function: h(t) = -16t² + 32t + 5

Interpretation: -16t² (gravity), +32t (initial velocity), +5 (initial height)

Find: Maximum height and when it hits the ground

2. Modeling Real-World Scenarios
3. Average Rate of Change
4. Domain and Range in Context
5. Function Composition
6. Common Application Types
7. Solving Word Problems
8. Problem-Solving Strategies
Frequently Asked Questions

Practice Time!

Practice Quiz
10
Questions
0
Correct
0%
Score
1
What is the average rate of change of f(x) = 3x + 5 from x = 1 to x = 4?
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2
A car travels at 60 mph. What function models distance after t hours?
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3
If f(x) = x² - 2x, what is f(3)?
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4
What type of function models exponential growth?
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5
The average rate of change of a linear function is:
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6
If a ball is thrown upward with h(t) = -16t² + 64t + 5, what is the maximum height?
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7
What does the domain of a function represent?
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8
If f(x) = 2x + 3 and g(x) = x - 1, what is f(g(2))?
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9
A population doubles every 5 years. If initial population is 1000, what is it after 15 years?
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10
What is the range of f(x) = x² + 3?
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