How to Graph a Piecewise Function on the TI-84 Evo

The TI-84 Evo has a piecewise template that keeps each piece of a function on its own row, with that piece's condition right beside it.

Type the piecewise function

As an example, this graphs a function with three pieces:

Piece Condition
y = x + 2 x < −3
y = x² −3 ≤ x < 3
y = 8 − x x ≥ 3
  1. Press y=. The cursor starts on Y1. If Y1 already holds a function, press clear to empty it. (New to graphing on the Evo? Graphing a function on the TI-84 Evo covers the basics.)
  2. Press math, then press the up arrow twice. The list wraps around to the bottom and stops on piecewise(.
    The TI-84 Evo MATH menu with B: piecewise( highlighted, just above C: Numeric Solver
  3. Press enter. A box asks how many PIECES the function has.
    The TI-84 Evo PIECES box over the MATH menu, with OK and CLEAR buttons
  4. Press the right or left arrow until PIECES reads 3, then press enter. The template appears on Y1 with one row per piece. In each row, the left box holds the piece and the right box holds its condition.
    An empty three-row piecewise template on the Y1 line of the TI-84 Evo Y= editor
  5. Type the first piece, then press the right arrow. For x + 2, press X, +, 2. The right arrow moves the cursor into the condition box.
    The first row of the piecewise template reading X+2, with the cursor in its condition box
  6. Press 2nd, then math, then the left arrow. The blue =≤≠> label above math opens the TEST menu, and the left arrow wraps around to its CONDITIONS tab, where every inequality already has the X in it.
  7. Scroll down to X< and press enter.
    The CONDITIONS tab of the TI-84 Evo TEST menu with item 2, X less than, highlighted
  8. Type −3. The first row now reads X+2; X<−3.
    The first row of the piecewise template complete: X+2 when X is less than negative 3
  9. Press the right arrow, then type x². The right arrow moves down to the second row. For x², press X, then x².
  10. Press the right arrow, then type −3. This condition has a number on each side of x, so type the left one first.
    The second row of the template with X squared typed and negative 3 started in its condition box
  11. Press 2nd, math and the left arrow again, then scroll down to ≤X<. On OS 7.0 this item reads ≤X and X< instead.
    The CONDITIONS tab with item 7, less than or equal to X less than, highlighted
  12. Press enter, then type 3. The second row now reads X²; −3≤X<3.
    The second row of the template complete: X squared when negative 3 is less than or equal to X and X is less than 3
  13. Press the right arrow, type 8 − x, and press the right arrow again. For 8 − x, press 8, −, X. The cursor moves down to the third row, then into its condition box.
  14. Press 2nd, math and the left arrow, choose X≥, and type 3. All three rows are filled in.
    The finished piecewise function on Y1: X+2 when X is less than negative 3, X squared from negative 3 up to 3, and 8 minus X when X is at least 3
  15. Press graph. Each piece is drawn only where its condition is true.
    The TI-84 Evo graph of the three-piece function: a rising line on the left, a parabola in the middle and a falling line on the right

Check the endpoints in the table

The graph has no open or closed dots where a piece ends, so it can't tell you which piece owns x = −3 or x = 3. The table can. Press 2nd, then graph (TABLE is the blue label above it), and press the up arrow until the cursor reaches X = −3.

The TI-84 Evo table for the piecewise function, X from negative 3 to 7: Y1 is 9 at X equals negative 3 and 5 at X equals 3
  • At X = −3, Y1 is 9. That's (−3)², from x², so −3 belongs to the middle piece: a closed dot on the parabola and an open dot at the end of the left line.
  • At X = 3, Y1 is 5. That's 8 − 3, from 8 − x, so 3 belongs to the right piece: a closed dot on the right line and an open dot at the end of the parabola.

Good to know

  • Each piece can have its own color. Put every piece on its own Y= line, each as a piecewise( with PIECES set to 1. Y1, Y2 and Y3 graph in blue, red and black.
    The same piecewise function graphed from three Y= lines, with the left line in blue, the parabola in red and the right line in black
  • The TEST tab has the plain signs. If you'd rather type the X yourself, press X, then 2nd, math and pick the sign from TEST. The condition comes out the same.
  • A missing stretch of graph usually means a gap in the conditions. Any x that no condition covers shows ERROR in the table, and nothing is drawn there.
  • A piece running off the screen? Adjust the graphing window to see all of it.