Math Practice

Increasing and Decreasing Intervals Practice Problems

Read each graph from left to right and give the x-values where it rises, falls or stays flat, in interval notation. Turning points are the boundaries.

Questions

1.
On what interval is increasing? Use interval notation (type oo for ∞).
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The slope 2 is positive, so the line rises everywhere: .
2.
On what interval is decreasing?
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The slope −4 is negative, so the line falls everywhere.
3.
The parabola has its vertex at . On what interval is it increasing?
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It opens up, so it rises to the right of the vertex: .
4.
For the same parabola , on what interval is it decreasing?
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It falls to the left of the vertex: .
5.
On what interval is increasing?
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Vertex , opening down: it rises up to .
6.
On what interval is decreasing?
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Vertex , opening up: it falls until .
7.
On what interval is increasing?
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The V has its corner at and rises to the right.
8.
On what interval is decreasing?
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Vertex at , opening up: decreasing on .
9.
The graph of turns at and . On what interval is it decreasing?
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It rises to , falls to , then rises: decreasing on .
10.
The graph of turns at and . Where is it increasing? Join two intervals with U.
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It rises before and after : .
11.
A graph rises from to , stays at height 5 until , then falls to . On what interval is it constant?
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The flat stretch runs from to .
12.
For the same graph, on what interval is it decreasing?
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It falls from to .

Written by

Zohaib

MPhil in Mathematics, Founder of Mathovia

Published

2 October 2026

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Increasing and Decreasing Intervals Practice Problems

These problems follow the increasing and decreasing intervals lesson. Type infinity as oo, and join separate intervals with U, for example (-oo, -2) U (2, oo).

Quick reference

Function	Increasing on	Decreasing on
,
,

Common mistakes to watch for

Giving -intervals. Intervals of increase and decrease are written with -values.
Including turning points. Use open intervals: the function is neither increasing nor decreasing exactly at a peak or valley.
Reading right to left. Always read the graph from left to right.
Ignoring constant sections. Flat parts of a graph are constant, not increasing.

Frequently Asked Questions

Do I use x-values or y-values?+

Always x-values. The intervals describe which inputs the function rises or falls over.

Parentheses or brackets at the turning points?+

Parentheses are the usual convention, but brackets at a turning point are accepted here too.

How do I type my answers?+

Type numbers without units, fractions like 5/3, and expressions like 2x + h. For intervals use parentheses or brackets and oo for infinity, for example (2, oo).

↗↘Increasing and Decreasing Intervals Practice Problems

Increasing and Decreasing Intervals Practice Problems

Quick reference

Common mistakes to watch for

Frequently Asked Questions

More practice problems

Increasing and Decreasing Intervals Practice Problems