Introduction to Functions
What You’ll Learn
Section titled “What You’ll Learn”In this first Algebra 2 lesson you’ll review what a function is, practice function notation, and learn how to evaluate and interpret functions in real-world contexts.
The Concept
Section titled “The Concept”A function is a rule that assigns exactly one output to each input. Think of it as a machine: you put in an input (x), and it gives you exactly one output (f(x)).
Function notation: we write the function as and read it as “f of x.”
Example:
This means: whatever number you put in for x, multiply it by 2 and then add 3.
To evaluate a function, replace x with a number and simplify:
Functions can represent real relationships such as cost, distance, temperature, or profit.
Worked Example
Section titled “Worked Example”1. Evaluate a linear function
Given , find .
2. Evaluate a quadratic function
Given , find .
3. Real-world function
A phone plan costs 30 dollars plus 0.10 dollars per text. Write this as a function and find the cost for 250 texts.
Let where t is the number of texts.
Real-World Application
Section titled “Real-World Application”Functions help model many everyday situations:
- Monthly phone or streaming bill based on usage
- Distance traveled = speed × time
- Cost of renting a car = daily fee + miles driven
- Profit = revenue − expenses
Being comfortable with function notation makes it much easier to work with these real-life relationships in later topics like quadratics, exponentials, and logarithms.