Piecewise Functions, step by step
A piecewise function applies a different rule depending on the input.
- READ THE CONDITIONSEach rule applies only on its own interval.
- PICK THE RIGHT PIECETo evaluate, check which interval the input falls in first.
- GRAPH EACH PIECE SEPARATELYOnly over its own interval, not the whole axis.
- MARK THE ENDPOINTSFilled circle if the endpoint is included, open if not.
worked
- f(x) = x + 1 for x < 2; f(x) = x² for x ≥ 2
- f(0) = 1 (first piece)
- f(3) = 9 (second piece)
Absolute value is a piecewise function in disguise: x for x ≥ 0, and −x for x < 0.
Questions about the Piecewise Functions poster
- What’s on the Piecewise Functions poster?
- 4 numbered steps, with a full worked run-through. A piecewise function applies a different rule depending on the input. READ THE CONDITIONS — Each rule applies only on its own interval.; PICK THE RIGHT PIECE — To evaluate, check which interval the input falls in first.; GRAPH EACH PIECE SEPARATELY — Only over its own interval, not the whole axis.; MARK THE ENDPOINTS — Filled circle if the endpoint is included, open if not.. Absolute value is a piecewise function in disguise: x for x ≥ 0, and −x for x < 0.
- Who is the Piecewise Functions poster for?
- Piecewise Functions is filed under 10th Grade (ages 15–16), so it matches what that year asks a child to remember. It is equally useful to an older student revisiting math, and to the parent or teacher answering the question at the kitchen table.
- When should you use the Piecewise Functions poster?
- Check the endpoints. Open or closed circles are where the marks are. A wall chart earns its place by being glanceable from where the work is happening, so Piecewise Functions belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Piecewise Functions?
- Sequences and Series, Completing the Square and Complex Numbers sit alongside Piecewise Functions in the 10th Grade set. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Sequences and SeriesCompleting the SquareComplex Numbers
- Is the Piecewise Functions poster free to download and print?
- Yes. Piecewise Functions downloads as a free PDF with no account, no email and no watermark, like everything else in the 10th Grade set. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
- What size does the Piecewise Functions poster print at?
- Piecewise Functions is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Piecewise Functions loses nothing.Printing guide
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Browse every 10th Grade poster, or start from the full catalogue.