Decreasing function

Definition

A decreasing function is one where the value of the function decreases as the input increases. For any two points $x_1$ and $x_2$ where $x_1 < x_2$, $f(x_1) \geq f(x_2)$.

5 Must Know Facts For Your Next Test

1. A linear function $f(x) = mx + b$ is decreasing if its slope $m$ is negative.
2. In a graph of a decreasing function, as you move from left to right, the graph goes downward.
3. The derivative of a decreasing function is less than or equal to zero on its domain.
4. For a continuous function, being strictly decreasing means that for any two points $x_1 < x_2$, we have $f(x_1) > f(x_2)$.
5. In interval notation, if a function is decreasing over $(a, b)$, it means that for every pair of numbers within this interval, the above conditions hold.

Review Questions

• What condition on the slope of a linear function makes it a decreasing function?
• How can you identify a decreasing function from its graph?
• What does it mean for the derivative of a decreasing function?

Related terms

Linear Function:

A polynomial function of degree one defined by $f(x) = mx + b$, where $m$ and $b$ are constants.

Derivative:

A measure of how a function changes as its input changes; often denoted as $f'(x)$ or $\frac{d}{dx} f(x)$.

Monotonic Function:

A function that is either entirely non-increasing or non-decreasing throughout its domain.