Worksheets · Algebra 2

Graphing piecewise functions worksheet for Algebra 2

Algebra 2 piecewise graphs mix lines and flat pieces, sometimes three of them, and the pieces do not always meet at the split. Each one is drawn only over its own condition, and the open or filled circle at each boundary shows which piece owns that x.

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

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Pick more than one for a sheet that mixes them.

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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)={−xx<22xx≥2−10−10−5−5551010
  2. Graph f(x)={−2x+4x<4−x−1x≥4−10−10−5−5551010
  3. Graph f(x)={−x+4x<0−x+3x≥0−10−10−5−5551010
  4. Graph f(x)={−2xx<−1x−4x≥−1−10−10−5−5551010
  5. Graph f(x)={−2xx<1−x+4x≥1−10−10−5−5551010
  6. Graph f(x)={2x−3x<2x−1x≥2−10−10−5−5551010
  7. Graph f(x)={x+1x<0x−4x≥0−10−10−5−5551010
  8. Graph f(x)={x+2x<−3x−3x≥−3−10−10−5−5551010
  9. Graph f(x)={−x+1x<2x+4x≥2−10−10−5−5551010
  10. Graph f(x)={2x−4x<02x−4x≥0−10−10−5−5551010

  1. Graph a three-piece function

    Graph f(x)={x+5x<−2−5−2≤x<2−x−5x≥2−10−10−5−5551010
  2. Graph f(x)={−2x−3x<−14−1≤x<32x−1x≥3−10−10−5−5551010
  3. Graph f(x)={x−1x<−44−4≤x<2−2x−1x≥2−10−10−5−5551010
  4. Graph f(x)={x+1x<−3−5−3≤x<4x−3x≥4−10−10−5−5551010
  5. Graph f(x)={x−1x<−55−5≤x<2−x−5x≥2−10−10−5−5551010
  6. Graph f(x)={x+2x<−41−4≤x<1x−2x≥1−10−10−5−5551010
  7. Graph f(x)={2x+2x<−30−3≤x<5xx≥5−10−10−5−5551010
  8. Graph f(x)={−x+1x<−43−4≤x<5−x+1x≥5−10−10−5−5551010
  9. Graph f(x)={−x−3x<−10−1≤x<1x−3x≥1−10−10−5−5551010
  10. Graph f(x)={2x+4x<−45−4≤x<1−2x+3x≥1−10−10−5−5551010

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

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Piecewise FunctionsAnswer keyVersion 2

Date Period

Graph each function.

  1. Graph a piecewise function

    Graph f(x)={−xx<22xx≥2−10−10−5−5551010Split at x=2: open circle at (2,−2), filled at (2,4)
  2. Graph f(x)={−2x+4x<4−x−1x≥4−10−10−5−5510105Split at x=4: open circle at (4,−4), filled at (4,−5)
  3. Graph f(x)={−x+4x<0−x+3x≥0−10−10−5−5510105Split at x=0: open circle at (0,4), filled at (0,3)
  4. Graph f(x)={−2xx<−1x−4x≥−1−10−10−5551010Split at x=−1: open circle at (−1,2), filled at (−1,−5)
  5. Graph f(x)={−2xx<1−x+4x≥1−10−10−5−5510105Split at x=1: open circle at (1,−2), filled at (1,3)
  6. Graph f(x)={2x−3x<2x−1x≥2−10−10−5551010−5Split at x=2: the pieces meet at (2,1), filled
  7. Graph f(x)={x+1x<0x−4x≥0−10−10−5−5551010Split at x=0: open circle at (0,1), filled at (0,−4)
  8. Graph f(x)={x+2x<−3x−3x≥−3−10−10−5−5551010Split at x=−3: open circle at (−3,−1), filled at (−3,−6)
  9. Graph f(x)={−x+1x<2x+4x≥2−10−10−5−5551010Split at x=2: open circle at (2,−1), filled at (2,6)
  10. Graph f(x)={2x−4x<02x−4x≥0−10−10−5551010−5Split at x=0: the pieces meet at (0,−4), filled

  1. Graph a three-piece function

    Graph f(x)={x+5x<−2−5−2≤x<2−x−5x≥2−10−10551010−5−5Open circle at (−2,3); flat from (−2,−5) filled to (2,−5) open; filled at (2,−7)
  2. Graph f(x)={−2x−3x<−14−1≤x<32x−1x≥3−10−10−5−5551010Open circle at (−1,−1); flat from (−1,4) filled to (3,4) open; filled at (3,5)
  3. Graph f(x)={x−1x<−44−4≤x<2−2x−1x≥2−10−10−5−5551010Open circle at (−4,−5); flat from (−4,4) filled to (2,4) open; filled at (2,−5)
  4. Graph f(x)={x+1x<−3−5−3≤x<4x−3x≥4−10−10−5551010−5Open circle at (−3,−2); flat from (−3,−5) filled to (4,−5) open; filled at (4,1)
  5. Graph f(x)={x−1x<−55−5≤x<2−x−5x≥2−10−10−5−5510105Open circle at (−5,−6); flat from (−5,5) filled to (2,5) open; filled at (2,−7)
  6. Graph f(x)={x+2x<−41−4≤x<1x−2x≥1−10−10−5−5551010Open circle at (−4,−2); flat from (−4,1) filled to (1,1) open; filled at (1,−1)
  7. Graph f(x)={2x+2x<−30−3≤x<5xx≥5−10−10−5−551010Open circle at (−3,−4); flat from (−3,0) filled to (5,0) open; filled at (5,5)
  8. Graph f(x)={−x+1x<−43−4≤x<5−x+1x≥5−10−10−5−5551010Open circle at (−4,5); flat from (−4,3) filled to (5,3) open; filled at (5,−4)
  9. Graph f(x)={−x−3x<−10−1≤x<1x−3x≥1−10−10−5−5551010Open circle at (−1,−2); flat from (−1,0) filled to (1,0) open; filled at (1,−2)
  10. Graph f(x)={2x+4x<−45−4≤x<1−2x+3x≥1−10−10−5−5510105Open circle at (−4,−4); flat from (−4,5) filled to (1,5) open; filled at (1,1)

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

How to do these

Graph f(x)={−x+1x≤2x−4x>2

  1. At x = 2 the first piece gives -1, and its condition includes 2, so (2, -1) is filled.
  2. The second piece gives -2 at x = 2 but does not include it, so (2, -2) is open.
  3. Draw each line away from the split on its own side.

The answer is Split at x=2: filled circle at (2,−1), open at (2,−2).

Where students go wrong

Evaluating only one piece at the split. Work out both: here they give -1 and -2, so the graph jumps and needs two circles at different heights.

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.

Algebra 2 is usually taken around 10th or 11th 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.