Increasing, decreasing, even and odd functions
Find the intervals where a graph rises or falls, reflect points in the y-axis and through the origin, and use f(-x) to test whether a function is even, odd or neither.
- France: grade 10
- Germany: grade 10
- Iran: grade 12
- Afghanistan: grade 10
- Syria: grade 10
- Palestine: grade 10
- Ukraine: grade 9
- Russia: grade 9
Guide
As x grows from left to right, a graph that goes up shows an increasing function and one that comes down a decreasing function. Give the interval in x, not y: for y = (x − 1)2 the function is increasing on [1, ∞).
A function is even function if f(−x) = f(x): its graph is symmetric in the y-axis. It is odd function if f(−x) = −f(x): its graph has half-turn symmetry about the origin.
To test, work out f(x) and f(−x) and compare. If they are neither equal nor opposite, the function is neither even nor odd.