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
Monotonicity of Functions
Monotonicity of Functions
Finding monotonicity from a graph and a table
Finding monotonicity from a graph and a table
- From a graph, follow the curve from left to right and write down the interval where it rises (increasing) and the interval where it falls (decreasing).
- The turning point, a peak or a valley, separates the two intervals.
- From a table of values, compare each output with the next one.
- If f(x) keeps increasing as x increases, the function is increasing on that part of the table.
- If the outputs decrease, the function is decreasing there.
| x | −2 | −1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|
| f(x) | 4 | 1 | 0 | 1 | 4 | 9 |
- From the table
- f decreases from x = −2 to x = 0
- and
- increases from x = 0 to x = 3.
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