Curriculum
Pure Mathematics — Second Secondary
Unit 1: Real Functions and Curve Sketching
0/8
Unit 2: Exponents and Logarithms
0/12
Unit 3: Limits
0/6
Unit 4: Trigonometry
0/4
Text lesson
Properties of Functions
Properties of Functions
One-to-one functions
One-to-one functions
- A one-to-one function gives different outputs for different inputs. In symbols: if f(a) = f(b), then a = b.
- The graphical test is the horizontal line test.
- If any horizontal line meets the graph in more than one point, the function is not one-to-one.
- Only one-to-one functions have inverse functions.
| Function | One-to-one? | Reason |
|---|---|---|
| f(x) = 2x + 3 | Yes | 2a + 3 = 2b + 3 gives a = b |
| f(x) = x² | No | f(2) = f(−2) = 4 |
| f(x) = x³ | Yes | A horizontal line meets the graph only once |
Properties of Functions · 2 / 5