Worksheets · Precalculus

Graphing piecewise functions worksheet for Precalculus

Each piece is an ordinary graph drawn over part of the line only. All the work is at the join: one piece owns that x and the other stops just short of it, which is what the open and filled circles are saying.

Also taught in Algebra 2, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Piecewise Functions

Date Period

Graph each function.

  1. Graph a piecewise function

    Graph f(x)={−2x+4x<1x+1x≥1−10−10−5−5551010
  2. Graph f(x)={−x+2x<0−x−4x≥0−10−10−5−5551010
  3. Graph f(x)={−x−3x<−22x−3x≥−2−10−10−5−5551010
  4. Graph f(x)={−2xx<32x−3x≥3−10−10−5−5551010
  5. Graph f(x)={2x−4x<12x−2x≥1−10−10−5−5551010
  6. Graph f(x)={−x+2x<−3xx≥−3−10−10−5−5551010
  7. Graph f(x)={x+2x<−4x−2x≥−4−10−10−5−5551010
  8. Graph f(x)={x−2x<−4−2x−2x≥−4−10−10−5−5551010
  9. Graph f(x)={2x+1x<−4−x−4x≥−4−10−10−5−5551010
  10. Graph f(x)={x+3x<−3x+4x≥−3−10−10−5−5551010

  1. Graph a three-piece function

    Graph f(x)={x+1x<−2−4−2≤x<3−x−4x≥3−10−10−5−5551010
  2. Graph f(x)={x−2x<−32−3≤x<32x−3x≥3−10−10−5−5551010
  3. Graph f(x)={2x+5x<−25−2≤x<5x−5x≥5−10−10−5−5551010
  4. Graph f(x)={−2x−2x<−2−1−2≤x<5−x−2x≥5−10−10−5−5551010
  5. Graph f(x)={x−2x<−52−5≤x<2x−4x≥2−10−10−5−5551010
  6. Graph f(x)={x+5x<−36−3≤x<2x−3x≥2−10−10−5−5551010
  7. Graph f(x)={2x+2x<−13−1≤x<2−x−2x≥2−10−10−5−5551010
  8. Graph f(x)={2x+3x<−26−2≤x<4−2x+5x≥4−10−10−5−5551010
  9. Graph f(x)={−2x+1x<−23−2≤x<2x+3x≥2−10−10−5−5551010
  10. Graph f(x)={x−2x<−56−5≤x<3−xx≥3−10−10−5−5551010

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

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Piecewise FunctionsAnswer keyVersion 1

Date Period

Graph each function.

  1. Graph a piecewise function

    Graph f(x)={−2x+4x<1x+1x≥1−10−10−5−5510105Split at x=1: the pieces meet at (1,2), filled
  2. Graph f(x)={−x+2x<0−x−4x≥0−10−10−5−5551010Split at x=0: open circle at (0,2), filled at (0,−4)
  3. Graph f(x)={−x−3x<−22x−3x≥−2−10−10−5551010−5Split at x=−2: open circle at (−2,−1), filled at (−2,−7)
  4. Graph f(x)={−2xx<32x−3x≥3−10−10−5−5551010Split at x=3: open circle at (3,−6), filled at (3,3)
  5. Graph f(x)={2x−4x<12x−2x≥1−10−10−5551010−5Split at x=1: open circle at (1,−2), filled at (1,0)
  6. Graph f(x)={−x+2x<−3xx≥−3−10−10−5−5551010Split at x=−3: open circle at (−3,5), filled at (−3,−3)
  7. Graph f(x)={x+2x<−4x−2x≥−4−10−10−5−5551010Split at x=−4: open circle at (−4,−2), filled at (−4,−6)
  8. Graph f(x)={x−2x<−4−2x−2x≥−4−10−10−5−5551010Split at x=−4: open circle at (−4,−6), filled at (−4,6)
  9. Graph f(x)={2x+1x<−4−x−4x≥−4−10−10−5−5551010Split at x=−4: open circle at (−4,−7), filled at (−4,0)
  10. Graph f(x)={x+3x<−3x+4x≥−3−10−10−5−5551010Split at x=−3: open circle at (−3,0), filled at (−3,1)

  1. Graph a three-piece function

    Graph f(x)={x+1x<−2−4−2≤x<3−x−4x≥3−10−10−5−5551010Open circle at (−2,−1); flat from (−2,−4) filled to (3,−4) open; filled at (3,−7)
  2. Graph f(x)={x−2x<−32−3≤x<32x−3x≥3−10−10−5−5551010Open circle at (−3,−5); flat from (−3,2) filled to (3,2) open; filled at (3,3)
  3. Graph f(x)={2x+5x<−25−2≤x<5x−5x≥5−10−10−5−510105Open circle at (−2,1); flat from (−2,5) filled to (5,5) open; filled at (5,0)
  4. Graph f(x)={−2x−2x<−2−1−2≤x<5−x−2x≥5−10−10−5−551010Open circle at (−2,2); flat from (−2,−1) filled to (5,−1) open; filled at (5,−7)
  5. Graph f(x)={x−2x<−52−5≤x<2x−4x≥2−10−10−5−5551010Open circle at (−5,−7); flat from (−5,2) filled to (2,2) open; filled at (2,−2)
  6. Graph f(x)={x+5x<−36−3≤x<2x−3x≥2−10−10−5551010−5Open circle at (−3,2); flat from (−3,6) filled to (2,6) open; filled at (2,−1)
  7. Graph f(x)={2x+2x<−13−1≤x<2−x−2x≥2−10−10−5−5551010Open circle at (−1,0); flat from (−1,3) filled to (2,3) open; filled at (2,−4)
  8. Graph f(x)={2x+3x<−26−2≤x<4−2x+5x≥4−10−10−5−5551010Open circle at (−2,−1); flat from (−2,6) filled to (4,6) open; filled at (4,−3)
  9. Graph f(x)={−2x+1x<−23−2≤x<2x+3x≥2−10−10−5−5551010Open circle at (−2,5); flat from (−2,3) filled to (2,3) open; filled at (2,5)
  10. Graph f(x)={x−2x<−56−5≤x<3−xx≥3−10−10−5−5551010Open circle at (−5,−7); flat from (−5,6) filled to (3,6) open; filled at (3,−3)

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

How to do these

Graph f(x)={2x+1x<1−x+4x≥1

  1. Draw y = 2x + 1 but stop before x = 1, with an open circle at (1, 3).
  2. Draw y = -x + 4 from x = 1 onwards, with a filled circle at (1, 3).
  3. Here they meet, so the two circles sit on the same point.

The answer is Split at x=1: open circle at (1,3), filled at (1,3).

Where students go wrong

Drawing each piece across the whole grid. Each one lives only on its own stretch of x. The other slip is filling both circles at the split: only the piece whose condition includes that x gets the solid one.

Also called piecewise graphs, plotting piecewise functions or open and closed circles.

What you can put on this worksheet

A piecewise function
Graph f(x)={2x−4x<0−2x−2x≥0 → Split at x=0: open circle at (0,−4), filled at (0,−2)
Three pieces, one of them flat
Graph f(x)={x+2x<−1−1−1≤x<32x−1x≥3 → Open circle at (−1,1); flat from (−1,−1) filled to (3,−1) open; filled at (3,5)
Three slanted pieces, other families, a single point
Graph f(x)={−2x+2x<−12x−3−1≤x<3−xx≥3 → Endpoints:
(−1,4) open,
(−1,−5) closed,
(3,3) open,
(3,−3) closed

Questions about these worksheets

Yes. Every graphing piecewise functions 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 graphing piecewise functions 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 two 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 3: a piecewise function, three pieces, one of them flat and three slanted pieces, other families, a single point. Tick as many as you want and set how many of each, or let it spread them evenly.

Drawing each piece across the whole grid. Each one lives only on its own stretch of x. The other slip is filling both circles at the split: only the piece whose condition includes that x gets the solid one.