WorksheetsPiecewise and Step Functions
Total questions: 36
Worksheet time: 1hrs 13mins
Name
Class
Date
1.
What is the RANGE of the function?
a)
(-∞, +∞)
b)
(-∞, 4]
c)
(-∞, 4)
d)
[0, 4]
2.
What is the DOMAIN of the function?
a)
(-∞, +∞)
b)
(-∞, 4]
c)
(-∞, 4)
d)
[0, 4]
3.
Using the pictured graph, what is f(-3)?
a)
-3
b)
-1
c)
1
d)
3
4.
What is g(7) if:
a)
-17
b)
-13
c)
13
d)
17
5.
What is f(-2)?
a)
4
b)
1
c)
-1
d)
7
6.
What is the DOMAIN of the function?
a)
(-∞, +∞)
b)
(-∞, -3) U (-3, +∞)
c)
(-∞, 2] U [3, +∞)
d)
(-∞, 3] U [3, +∞)
7.
What is the RANGE of the function?
a)
(-∞, +∞)
b)
(-∞, -3) U (-3, +∞)
c)
(-∞, 2] U [4, +∞)
d)
(-∞, 3] U [3, +∞)
8.
Give the parent function or function family.
a)
Quadratic
b)
Cubic
c)
Exponential
d)
Square Root
9.
What is f(x) when x equals 0?
a)
-5
b)
0
c)
1/2
d)
1
10.
What is f(x) when x equals 4?
a)
-5
b)
0
c)
3
d)
6
11.
What is g(x) when x equals -4?
a)
-16
b)
-3/2
c)
5/2
d)
16
12.
A piecewise function, f(x), is shown in the graph. What is f(x) when x equals -4?
a)
-4
b)
-2
c)
0
d)
Does not exist
13.
What is m(-3) if:
a)
-3
b)
0.5
c)
3
d)
-3.5
14.
How much does it cost to rent the Karaoke machine for 3 days?
a)
$50
b)
$100
c)
$150
d)
$175
15.
How much does it cost to make 300 photocopies?
a)
$24.00
b)
$20.00
c)
$40.00
d)
$300.00
16.
For what value of x is the function g equal to 4?
a)
-9
b)
0
c)
2
d)
g cannot equal 4
17.
What is f(-2)?
a)
4
b)
1
c)
1
d)
DNE
18.
Which piecewise function corresponds to this graph? (Take your time)
a)
f(x) = { x if x < 4; -x+1 if x ≥ 4
b)
f(x) = { x if x ≤ 4; -x+1 if x > 4
c)
f(x) = { -x+1 if x < 4; x if x ≥ 4
d)
f(x) = { -x+1 if x ≤ 4; x if x > 4
19.
a)
$12.75
b)
$35
c)
$45
d)
$27.75
20.
a)
$12.75
b)
$35
c)
$43.40
d)
$27.75
21.
Which of the 3 piecewise equations is depicted by the graph? (Take your time)
a)
f(x)
b)
g(x)
c)
h(x)
22.
Using the pictured graph, what is f(-3)?
a)
-3
b)
-1
c)
1
d)
3
23.
Which graph matches:
4−x, x<2
2x−6, x≥2 a)
A
b)
B
c)
C
d)
D
24.
What are the domain restrictions for the green piece of this function?
a)
-2 < x ≤ 1
b)
-1 < x ≤ 0.5
c)
x > -2
d)
x ≤ 1
25.
What is the equation of the graph below?
a)
f(x) = I x + 2 I
b)
f(x) = I x I + 2
c)
f(x) = I x I - 2
d)
f(x) = I x - 2 I
26.
y = |x| - 7 makes the graph slide . . .
a)
left 7
b)
right 7
c)
up 7
d)
down 7
27.
y = |x - 3| makes the graph slide . . .
a)
left 3
b)
right 3
c)
up 3
d)
down 3
28.
What is the vertex of the absolute value function?
a)
(4, 0)
b)
(0, 4)
c)
(−∞, ∞)
d)
[4,∞)
29.
What is the equation of the RED piece (one on the RIGHT)?
a)
x - 1 if x > 3
b)
3 if x ≥ 3
c)
-1 if x ≥ 3
d)
-1 if x > 3
30.
What is f(0)?
a)
0
b)
-2
c)
3
d)
+∞
31.
Which of the following best describes a step function?
a)
A step function has many steps which are required for solving the function.
b)
A step function is not actually a function because it does not pass the vertical line test at all points.
c)
A step function is a piecewise function that is constant over each interval of the domain.
d)
A step function has many horizontal and vertical lines which contribute to the function as a whole.
32.
This piecewise function is a combination of at least how many functions?
a)
0
b)
1
c)
2
d)
3
33.
What is this type of function called? (Select all that apply.)
a)
Floor Function
b)
Segment Function
c)
Step Function
d)
Jump Function
34.
What is the range of the function?
a)
(-∞,4]
b)
(-∞,∞)
c)
[4, ∞)
d)
(4,∞)
35.
What is the Domain and Range of the Function?
a)
D:[2,∞)
R:[0,∞)
R:[0,∞)
b)
D: All Real numbers
R:[0,∞)
R:[0,∞)
c)
D:(2,∞)
R:(0,∞)
R:(0,∞)
d)
D:All Real Numbers
R:(0,∞)
R:(0,∞)
36.
What is the equation of the graph below?
a)
f(x ) = I x + 4 I + 2
b)
f(x ) = -I x - 4 I + 2
c)
f(x ) = I x - 4 I + 2
d)
f(x ) = -I x + 4 I + 2
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