Lesson 5: Intervals of Increase and Decrease

Property

A function is increasing on an interval if as $x$ values move from left to right, the $y$ values rise (positive slope).
A function is decreasing on an interval if as $x$ values move from left to right, the $y$ values fall (negative slope).

Examples

Property

A function is constant on an interval if its output value ($y$-value) does not change as the input value ($x$-value) increases.
On a graph, this appears as a horizontal line segment.

Examples

Property

The slope determines if the function is an increasing linear function, a decreasing linear function, or a constant function.

Examples

• The function $f(x) = 2x + 5$ is increasing because the slope $m=2$ is positive.
• The function $g(x) = -3x + 1$ is decreasing because the slope $m=-3$ is negative.
• The function $h(x) = 9$ is constant because the slope $m=0$. Its graph is a horizontal line.

Explanation

The sign of the slope tells you the direction of the line. A positive slope means the line goes uphill from left to right. A negative slope means it goes downhill. A zero slope means the line is perfectly flat.