Piecewise Functions Exit Ticket
CP Algebra 1 • Section 4-6
Piecewise & Step Functions Exit Ticket
Name: ______________________________
Date: ____________ Period: _____
1
Evaluate each greatest integer expression.
a) ⟦ 4.8 ⟧ =
Show or explain your thinking:
b) ⟦ −3.2 ⟧ =
Show or explain your thinking:
2
Graph the piecewise-defined function. Then state the domain and range.
\[ f(x) = \begin{cases} x + 2 & \text{if } x < 1 \\ -2x + 4 & \text{if } x \ge 1 \end{cases} \]
Domain:
Range:
y x 0
3
Apply a step function to a real-world situation.
A downtown parking garage charges $4 per hour to park. Every fraction of an hour is rounded up to the next whole hour.
a) How much does it cost to park for 2.5 hours?
Cost:
b) How much does it cost to park for 4 hours?
Cost:
Piecewise Functions Answer Key
CP Algebra 1 • Section 4-6
Piecewise & Step Functions Exit Ticket
Answer Key
1
Evaluate each greatest integer expression.
a) ⟦ 4.8 ⟧ =
4
Show or explain your thinking:
Greatest integer \(\le 4.8\) is \(4\).
b) ⟦ −3.2 ⟧ =
−4
Show or explain your thinking:
Greatest integer \(\le -3.2\) is \(-4\) (left on number line).
2
Graph the piecewise-defined function. Then state the domain and range.
\[ f(x) = \begin{cases} x + 2 & \text{if } x < 1 \\ -2x + 4 & \text{if } x \ge 1 \end{cases} \]
| x |
y |
| 1 (closed) |
2 |
| 2 |
0 |
| 3 |
−2 |
Domain:
All real numbers, or \((-\infty, \infty)\)
Range:
\(y < 3\), or \((-\infty, 3)\)
y x 0
3
Apply a step function to a real-world situation.
A downtown parking garage charges $4 per hour to park. Every fraction of an hour is rounded up to the next whole hour.
a) How much does it cost to park for 2.5 hours?
2.5 hours rounds up to 3 hours.
\( 3 \times \$4 = \$12 \)
Cost:
$12
b) How much does it cost to park for 4 hours?
4 hours is already a whole hour.
\( 4 \times \$4 = \$16 \)
Cost:
$16
