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Algebra 2
35. MA.912.F.1.7
35.1 One to one functions
One-to-One Functions
A one-to-one function maps each output back to exactly one input; test it with the horizontal line test.
What You'll Learn
A one-to-one function maps each output to exactly one input (an injective function).
Use the horizontal line test: no horizontal line may cross the graph more than once.
A line is one-to-one; a parabola is not (it fails the test).
Only one-to-one functions have inverse functions.
To test an equation, assume f(a)=f(b) and check that this forces a=b.
What You'll Practice
1
Testing graphs using horizontal and vertical line tests
2
Analyzing mapping diagrams to classify function types
3
Identifying one-to-many vs. many-to-one relationships
4
Determining whether functions are injective, surjective, or neither
Why This Matters
One-to-one functions are essential for understanding inverse functions and advanced algebra. This concept appears throughout calculus, discrete math, and is foundational for proving mathematical relationships and solving equations.
Before You Start — Make Sure You Can:
This Unit Includes
4 Video lessons
Practice exercises
Learning resources
Skills
One-to-One Functions
Injective Functions
Surjective Functions
Horizontal Line Test
Vertical Line Test
Function Mapping
Domain and Range
FL Curriculum Aligned