Algebra 2 / Unit 1: Functions and Transformations
1.3 Piecewise Functions
Notes
A piecewise function uses different rules on different parts of the domain.
- Example: $f(x) = \begin{cases} x^2 & x < 1 \\ 2x + 3 & x \ge 1 \end{cases}$
- To evaluate, first find which condition the input meets, then use only that rule.
- $f(-3) = (-3)^2 = 9$ and $f(1) = 2(1) + 3 = 5$.
- A step function like a parking fee is a piecewise function with flat pieces.
Practice
For $f(x) = \begin{cases} x^2 & x < 1 \\ 2x + 3 & x \ge 1 \end{cases}$, find $f(1)$.
$x = 1$ meets $x \ge 1$, so use $2(1) + 3$.
For the same function, find $f(-3)$.
$-3 < 1$, so use $x^2$: $(-3)^2 = 9$.
A phone plan costs $30 for up to 2 GB of data, then $10 for each GB over 2 GB, so $C(g) = 30 + 10(g - 2)$ for $g > 2$. What is the cost for 3.5 GB?
$30 + 10(1.5) = 45$.
Ready for more? Take the Unit 1 test.