Skip to content

Understanding Functions

Define functions, identify them from tables, graphs, and equations.

Written and reviewed by the Study Mondo Education TeamLast updated
🎯⭐ INTERACTIVE LESSON

Try the Interactive Version!

Learn step-by-step with practice exercises built right in.

Start Interactive Lesson →

Understanding Functions

What Is a Function?

A function is a rule that assigns to each input exactly one output.

Input→functionOutput\text{Input} \xrightarrow{\text{function}} \text{Output}

Function Notation

f(x)f(x) means "the output of function ff when the input is xx."

If f(x)=2x+3f(x) = 2x + 3:

  • f(1)=2(1)+3=5f(1) = 2(1) + 3 = 5
  • f(4)=2(4)+3=11f(4) = 2(4) + 3 = 11
  • f(−2)=2(−2)+3=−1f(-2) = 2(-2) + 3 = -1

Is It a Function?

Table test: Each input has only ONE output.

InputOutputFunction?
1 → 3, 2 → 5, 3 → 7✅ YesEach input has one output
1 → 3, 2 → 5, 1 → 7❌ NoInput 1 has two outputs

Vertical Line Test: If any vertical line crosses the graph more than once, it's NOT a function.

Linear vs. Nonlinear Functions

Linear: Graph is a straight line, constant rate of change. f(x)=mx+bf(x) = mx + b

Nonlinear: Graph is curved, rate of change varies. f(x)=x2,f(x)=x,f(x)=∣x∣f(x) = x^2, \quad f(x) = \sqrt{x}, \quad f(x) = |x|

Comparing Functions

Functions can be represented as:

  1. Equations: y=3x+1y = 3x + 1
  2. Tables: pairs of (x,y)(x, y) values
  3. Graphs: visual representation
  4. Verbal descriptions: "3 times a number plus 1"

Compare functions by examining their rates of change (slopes) and initial values (y-intercepts).

Key idea: A function is like a machine — put in an input, get exactly one output. No input gives two different outputs!

Explain using:
Next Topic →
Slope and Linear Functions
🎴

Practice with Flashcards

Rate this topic's cards with spaced repetition. Cards join your deck when you finish a topic's lesson and take its exit quiz.

📖

Browse All Topics

Explore more Grade 8 Math topics

📌 Related Topics in Functions

Slope and Linear Functions

❓ Frequently Asked Questions

What is Understanding Functions?▾
Define functions, identify them from tables, graphs, and equations.
How can I study Understanding Functions effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Regular review and active practice are key to retention.
Is this Understanding Functions study guide free?▾
Yes — all study notes, flashcards, and practice problems for Understanding Functions on Study Mondo are free to access. No account is needed.
What course covers Understanding Functions?▾
Understanding Functions is part of the Grade 8 Math course on Study Mondo, specifically in the Functions section. You can explore the full course for more related topics and practice resources.