Before you read

Answer first — see what you already know.

If $f (x) = {3 x - 1 x^{2} x < 2 x \geq 2$ , what is $f (2)$ ?

A
$4$
B
$5$
C
$3$
D
$7$

Check your answer

Answer:

Before you read

Answer first — see what you already know.

If $g (x) = ⎩ ⎨ ⎧ - x x + 2 5 x \leq 0 0 < x < 3 x \geq 3$ , what is $g (3)$ ?

A
$- 3$
B
$5$
C
$6$
D
$3$

Check your answer

Answer:

Theory

Piecewise Functions

A piecewise function uses different formulas for different parts of its domain:

$f(x) = \begin{cases} x^2 & \text{if } x < 0 \\ 2x + 1 & \text{if } x \geq 0 \end{cases}$

Piece 1: f(x) = x for x < 0

Piece 2: f(x) = -x + 4 for x ≥ 0

To evaluate: check which condition $x$ satisfies, then use that formula.

Example: $f(-3) = (-3)^2 = 9$ (use first piece since $-3 < 0$ )
$f(4) = 2(4) + 1 = 9$ (use second piece since $4 \geq 0$ )

Example 1

For the function above, find $f(0)$ .

$0 \geq 0$ , so use the second piece

$f(0) = 2(0) + 1 = 1$

f(0) = 1

Tip

ACT Pro Tip

On piecewise function questions, the most common mistake is using the wrong piece. Always check the inequality conditions carefully — pay attention to $<$ vs $\leq$ (open vs closed circle on the graph).

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