Worksheets · Precalculus

Increasing and decreasing intervals from a graph worksheet for Precalculus

Read the graph from left to right. It is increasing where it climbs and decreasing where it falls. A relative maximum is a point where it turns from rising to falling, and a relative minimum the reverse.

Also taught in Algebra 1, at its own level and with its own examples.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Increasing and Decreasing

Date Period

Answer each question, using the graph where one is given.

  1. The graph of f is shown. On what open intervals is f increasing?−4−3−2−1012345−3−2−10123f
  2. The graph of f is shown. Find every relative maximum point of f. Endpoints do not count.−4−3−2−1012345−3−2−10123f
  3. The graph of f is shown. On what open intervals is f decreasing?−3−2−10123456−3−2−10123f
  4. The graph of f is shown. Find every relative minimum point of f. Endpoints do not count.−2−101234567−3−2−10123f
  5. The graph of f is shown. Find every relative minimum point of f. Endpoints do not count.−3−2−10123456−3−2−10123f
  6. The graph of f is shown. Find every relative maximum point of f. Endpoints do not count.−3−2−10123456−3−2−10123f
  7. The graph of f is shown. On what open intervals is f increasing?−4−3−2−1012345−3−2−10123f
  8. The graph of f is shown. On what open intervals is f decreasing?−4−3−2−1012345−3−2−10123f
  9. The graph of f is shown. On what open intervals is f decreasing?−4−3−2−1012345−3−2−10123f
  10. The graph of f is shown. On what open intervals is f increasing?−3−2−10123456−3−2−10123f
  11. The graph of f is shown. Find every relative maximum point of f. Endpoints do not count.−1012345678−3−2−10123f
  12. The graph of f is shown. Find every relative minimum point of f. Endpoints do not count.−4−3−2−1012345−3−2−10123f
  13. The graph of f is shown. On what open intervals is f increasing?−3−2−10123456−3−2−10123f
  14. The graph of f is shown. On what open intervals is f decreasing?−5−4−3−2−101234−3−2−10123f
  15. The graph of f is shown. Find every relative maximum point of f. Endpoints do not count.−2−101234567−3−2−10123f
  16. The graph of f is shown. Find every relative minimum point of f. Endpoints do not count.−4−3−2−1012345−3−2−10123f
  17. The graph of f is shown. Find every relative maximum point of f. Endpoints do not count.−4−3−2−1012345−3−2−10123f
  18. The graph of f is shown. On what open intervals is f increasing?−1012345678−3−2−10123f
  19. The graph of f is shown. On what open intervals is f decreasing?−1012345678−3−2−10123f
  20. The graph of f is shown. Find every relative minimum point of f. Endpoints do not count.−2−101234567−3−2−10123f

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Increasing and DecreasingAnswer keyVersion 1

Date Period

Answer each question, using the graph where one is given.

  1. The graph of f is shown. On what open intervals is f increasing?−4−3−2−1012345−3−2−10123f(−4,0)∪(3,5)
  2. The graph of f is shown. Find every relative maximum point of f. Endpoints do not count.−4−3−2−1012345−3−2−10123f(1,3)
  3. The graph of f is shown. On what open intervals is f decreasing?−3−2−10123456−3−2−10123f(−2,2)
  4. The graph of f is shown. Find every relative minimum point of f. Endpoints do not count.−2−101234567−3−2−10123f(2,−3)
  5. The graph of f is shown. Find every relative minimum point of f. Endpoints do not count.−3−2−10123456−3−2−10123f(3,0)
  6. The graph of f is shown. Find every relative maximum point of f. Endpoints do not count.−3−2−10123456−3−2−10123f(2,0) and (4,3)
  7. The graph of f is shown. On what open intervals is f increasing?−4−3−2−1012345−3−2−10123f(−1,2)∪(3,4)
  8. The graph of f is shown. On what open intervals is f decreasing?−4−3−2−1012345−3−2−10123f(−3,−2)∪(0,2)
  9. The graph of f is shown. On what open intervals is f decreasing?−4−3−2−1012345−3−2−10123f(−3,2)
  10. The graph of f is shown. On what open intervals is f increasing?−3−2−10123456−3−2−10123f(2,5)
  11. The graph of f is shown. Find every relative maximum point of f. Endpoints do not count.−1012345678−3−2−10123f(1,2)
  12. The graph of f is shown. Find every relative minimum point of f. Endpoints do not count.−4−3−2−1012345−3−2−10123f(0,−1)
  13. The graph of f is shown. On what open intervals is f increasing?−3−2−10123456−3−2−10123f(−3,0)∪(2,5)
  14. The graph of f is shown. On what open intervals is f decreasing?−5−4−3−2−101234−3−2−10123f(−4,−2)∪(1,3)
  15. The graph of f is shown. Find every relative maximum point of f. Endpoints do not count.−2−101234567−3−2−10123f(0,3), (2,1), and (6,0)
  16. The graph of f is shown. Find every relative minimum point of f. Endpoints do not count.−4−3−2−1012345−3−2−10123f(1,0)
  17. The graph of f is shown. Find every relative maximum point of f. Endpoints do not count.−4−3−2−1012345−3−2−10123f(1,1)
  18. The graph of f is shown. On what open intervals is f increasing?−1012345678−3−2−10123f(5,8)
  19. The graph of f is shown. On what open intervals is f decreasing?−1012345678−3−2−10123f(0,2)∪(5,7)
  20. The graph of f is shown. Find every relative minimum point of f. Endpoints do not count.−2−101234567−3−2−10123f(5,0)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

A graph rises from x=−3 to x=1 and falls from 1 to 4. Where is it increasing?

  1. Intervals are written with x-values, not y-values.

The answer is (−3,1).

Where students go wrong

Giving the intervals in y-values. "Increasing on (−3, 1)" describes the x-values where the graph climbs.

Also called relative maximum and minimum from a graph.

What you can put on this worksheet

Increasing, decreasing and extrema from a graph
The graph of f is shown. On what open intervals is f decreasing? — the graph of f on [-4, 3] → (0,1)
Relative extrema on a smooth curve
Find the relative maxima and minima of the function graphed. → Relative maximum (1,3); relative minimum (−1,1)
Graphs that run off, or split at an asymptote
Give the intervals where the function graphed is increasing and where it is decreasing. → Increasing on (−∞,−2) and (1,∞); decreasing on (−2,1)
With a graphing calculator
Use a graphing calculator to approximate, to the nearest hundredth, the relative extrema of f(x)=−x3+3x2+x+5 → Relative maximum (2.15,11.08); relative minimum (−0.15,4.92)
Absolute maximum and minimum
Find the absolute maximum and minimum of the function graphed, if they exist. The graph continues forever. → Absolute maximum 1 at x=−3; no absolute minimum

Questions about these worksheets

Yes. Every increasing and decreasing intervals from a graph sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the increasing and decreasing intervals from a graph questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 5: increasing, decreasing and extrema from a graph, relative extrema on a smooth curve, graphs that run off, or split at an asymptote, with a graphing calculator and absolute maximum and minimum. Tick as many as you want and set how many of each, or let it spread them evenly.

Giving the intervals in y-values. "Increasing on (−3, 1)" describes the x-values where the graph climbs.