Solutions
Name ___________________________
Period ____ Date __________
Algebra III: 0.2 Piecewise Functions
Bell Work: What is the domain and range for each function?
y
a.
b.
Domain: 0 ≤ 𝑥 ≤ 3
(3,5)
Range: 0 ≤ 𝑦 ≤ 5
5
3
c.
y
y
Range: 𝑦 ≤ 3
(5, 3)
Domain: ℝ
Range: 𝑦 ≤ 5
x
Domain: 𝑥 ≤ 5
x
x
The data in the table represents a function, f. Using the table complete the following:
x
-1
4
5
7
10
f(x)
0
-3
2
6
1
1.
f (4) = -3
2.
If f ( 7 ) = 6
3.
What are the elements of the domain of f?
What are the elements of the range of f?
{−1, 4, 5, 7, 10}
{−3, 0, 1, 2, 6}
Using the graph of function h, complete the following:
5.
h(4) =
2
6. h(10) = 1
7. What is the domain of h?
(write an inequality)
0≤𝑥≤5
8. Which function (f or h) is discrete? f
Which function is continuous?
h
Piecewise Functions
If y = f (x), then create the graph of the
function f in your graphing calculator using.
The equation…
−2( x − 2), 0 ≤ x ≤ 2
3

)  ( x − 2), 2 ≤ x ≤ 4
f ( x=
2
3, 4 ≤ x ≤ 9
y
x
Write what you typed under Y1 – Y3 in the calculator.
9.
10.
Y1= −2(𝑥 − 2)/(𝑥 ≥ 0 𝑎𝑎𝑎 𝑥 ≤ 2)
between the x-axis and f
from x = 0 to x = 9.
3
Y2= (𝑥 − 2)/(𝑥 > 2 𝑎𝑎𝑎 𝑥 ≤ 4)
1
2
2
Y3= 3/(𝑥 > 4 𝑎𝑎𝑎 𝑥 ≤ 9)
11.
y
Graph f(x + 2)
Find the area bounded
𝟏
(2)(4) + (𝟐)(𝟑) +(𝟓)(𝟑)
𝟐
= 𝟐𝟐 square units
12.
y
Graph f(x) + 2
x
Describe how this graph compares to f.
The graph is translated left 2 units
x
Describe how this graph compares to f.
The graph is translated up 2 units