SAT Math · Study & Practice
Piecewise Functions
A piecewise function uses different rules over different parts of its domain. This chapter covers the definition, how to evaluate them, and how they look on a graph. Read each topic, work the problems with the hint ladder, then take the 8-question topic test.
Topics
Chapter test
Formula Reference Sheet
This chapter
Idea
| Definition | different rule on each interval of x |
|---|---|
| Choose the branch | see which interval the input falls in |
| Then evaluate | use only that branch’s rule |
Graph features
| Open circle | endpoint not included |
|---|---|
| Closed circle | endpoint included |
| Jump | a break between pieces (discontinuity) |
Digital SAT reference
Area & Circumference
| Circle area | A = πr² |
|---|---|
| Circle circumference | C = 2πr |
| Rectangle | A = ℓw |
| Triangle | A = ½ b h |
Volume
| Rectangular box | V = ℓwh |
|---|---|
| Cylinder | V = πr²h |
| Sphere | V = 4⁄3 πr³ |
| Cone | V = 1⁄3 πr²h |
| Pyramid | V = 1⁄3 ℓwh |
Right triangles
| Pythagorean theorem | a² + b² = c² |
|---|---|
| 30°–60°–90° | sides x : x√3 : 2x |
| 45°–45°–90° | sides s : s : s√2 |
Constants
| Degrees in a circle | 360° |
|---|---|
| Radians in a circle | 2π |
| Angles of a triangle | sum = 180° |
🖩 Graphing Calculator