Decreasing Function
College/University
Definition
Tells you the behaviour of a function. When the y-value of a function decreases as its x-value increases. This means that the graph is moving downwards as you go from left to right. Decreasing functions have negative slopes because of this.
Worked examples
\(f(x) = -2x + 5\)
As x increases, y decreases — the graph falls from left to right with slope \(-2\).
\(g(x) = -x^2\)
Decreasing on \((0, \infty)\) — the right side of the parabola falls as x increases.
Common mistakes
- \(f(x) = -3x + 1\) is increasing because the y-intercept is positive → \(f(x) = -3x + 1\) is decreasing because the slope is negative The sign of the slope, not the intercept, determines whether a linear function increases or decreases.
- A function is decreasing if it has any negative y-values → A function is decreasing if y decreases as x increases Decreasing describes the direction of change, not whether outputs are negative.
- \(h(x) = x^2\) is always decreasing because it opens down → \(h(x) = x^2\) is decreasing on \((-\infty, 0)\) and increasing on \((0, \infty)\) A parabola opening upward decreases on one interval and increases on another.
Where you'll use it next
Decreasing functions appear when analyzing graphs in algebra and pre-calculus, finding intervals of increase/decrease with derivatives in calculus, and modeling decay, depreciation, and cooling in applied problems.
Found in 1 StudyPug lesson
Curve sketching
UniversityUniversityCalculus 1
In this section we will expand our knowledge on the connection between derivatives and the shape of a graph. By following the "5-Steps Approach", we will quantify the characteristics of the function with application of derivatives, which will enable us to sketch the graph of a function.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026