#### Solved Examples and Worksheet for Graphing Piecewise and Step Functions

Q1Choose the graph of the piecewise function
f(x) = - cos x if x ≤ 0
= - ex if x > 0

A. Graph 4
B. Graph 2
C. Graph 1
D. Graph 3

Step: 1
f(x) = - cos x if x ≤ 0
= - ex if x > 0
[Write the function.]
Step: 2
The graph of the given piecewise function will be in two pieces.
Step: 3
The function f(x) = - cos x, if x ≤ 0, indicates that the graph begins when x = 0, and is to the left of the origin as shown.
Step: 4
The function f(x) = - ex, if x > 0, indicates that the graph begins when x > 0, which is to the right of the origin as shown.
Step: 5
Therefore, graph 1 represents the given piecewise function.
Correct Answer is :   Graph 1
Q2Choose the graph of the piecewise function
y = 4 if x ≤ 0
= 3x if 0 < x ≤ 1
= 1 - 2x if 1 < x < ∞

A. Graph 2
B. Graph 1
C. Graph 4
D. Graph 3

Step: 1
y = 4 if x ≤ 0
= 3x if 0 < x ≤ 1
= 1 - 2x if 1 < x < ∞
[Write the function.]
Step: 2
The graph of the given piecewise function will be in three pieces.
Step: 3
The function y = 4, if x ≤ 0 indicates that the graph is parallel to x axis at y = 4, begins when x = 0, and is to the left of the origin as shown.
Step: 4
The function y = 3x, if 0 < x ≤ 1 indicates that the graph begins when x > 0 and it touches y = 3 at x = 1, which is to the right of the origin as shown.
Step: 5
The function y = 1 - 2x, if 1 < x < ∞ indicates that the graph begins when x > 1, which is to the right of the orgin as shown.
Step: 6
Therefore, graph 2 represents the given piecewise function,
Correct Answer is :   Graph 2
Q3Choose the graph of the piecewise function
y = 2 if x ≤ 0
= x + 1 if 0 < x ≤ 3
= 5 - 2x if 3 < x < ∞

A. Graph 3
B. Graph 4
C. Graph 1
D. Graph 2

Step: 1
y = 2 if x ≤ 0
= x + 1 if 0 < x ≤ 3
= 5 - 2x if 3 < x < ∞
[Write the function.]
Step: 2
The graph of the given piecewise function will be in three pieces.
Step: 3
The function y = 2, if x ≤ 0 indicates that the graph is parallel to x axis at y = 2, begins when x = 0, and is to the left of the origin as shown.
Step: 4
The function y = x + 1 if 0 < x ≤ 3 indicates that the graph begins when x > 0 and it touches y = 4 at x = 3, which is to the right of the origin as shown.
Step: 5
The function y = 5 - 2x, if 3 < x < ∞ indicates that the graph begins when x > 3, which is to the right of the origin as shown.
Step: 6
Therefore, graph 3 represents the given piecewise function.
Correct Answer is :   Graph 3
Q4Choose the graph of the piecewise function
y = 3 if x ≤ 0
= - 3 if x > 0

A. Graph 3
B. Graph 1
C. Graph 2
D. Graph 4

Step: 1
y = 3 if x ≤ 0
= - 3 if x > 0
[Write the function.]
Step: 2
The graph of the given piecewise function will be in two pieces.
Step: 3
The function y = 3, if x ≤ 0 indicates that the graph is parallel to x axis at y = 3, begins when x = 0, and is to the left of the origin as shown.
Step: 4
The function y = - 3, if x > 0 indicates that the graph is parallel to x axis at y = -3, begins when x > 0, which is to the right of the origin as shown.
Step: 5
Therefore, graph 4 represents the given piecewise function.
Correct Answer is :   Graph 4
Q5Choose the graph of the piecewise function
y = x - 3 if x ≤ 2
= 2 if x > 2

A. Graph 3
B. Graph 1
C. Graph 2
D. Graph 4

Step: 1
y = x - 3 if x ≤ 2
= 2 if x > 2
[Write the function.]
Step: 2
The graph of the given piecewise function will be in two pieces.
Step: 3
The graph of the function y = x - 3, if x ≤ 2, is as shown.
Step: 4
The function y = 2, if x > 2 indicates that the graph is parallel to x axis at y = 2, begins when x > 2, which is to the right of the origin as shown.
Step: 5
Therefore, graph 1 represents the given piecewise function.
Correct Answer is :   Graph 1
Q6Choose the graph of the piecewise function
y = 3 if x ≤ 0
= x - 1 if 0 < x ≤ 2
= 8 - 3x if 2 < x < ∞

A. Graph 4
B. Graph 1
C. Graph 3
D. Graph 2

Step: 1
y = 3 if x ≤ 0
= x - 1 if 0 < x ≤ 2
= 8 - 3x if 2 < x < ∞
[Write the function.]
Step: 2
The graph of the given piecewise function will be in three pieces.
Step: 3
The function y = 3, if x ≤ 0 indicates that the graph is parallel to x axis at y = 3, begins when x = 0, and is to the left of the origin as shown.
Step: 4
The function y = x - 1 if 0 < x ≤ 2 indicates that the graph begins when x > 0 and it touches y = 1 at x = 2, which is to the right of the origin as shown.
Step: 5
The function y = 8 - 3x if 2 < x < ∞ indicates that the graph begins when x > 2, which is to the right of the origin as shown.
Step: 6
Therefore, graph 2 represents the given piecewise function.
Correct Answer is :   Graph 2
Q7Choose the graph of the piecewise function
y = |x| if x ≤ 0
= x2 if x > 0

A. Graph 1
B. Graph 3
C. Graph 2
D. Graph 4

Step: 1
y = |x| if x ≤ 0
= x2 if x > 0
[Write the function.]
Step: 2
The graph of the given piecewise function will be in two pieces.
Step: 3
The graph of the function y = |x|, if x ≤ 0, is as shown.
Step: 4
The graph of the function y = x2, if x > 0 , is as shown.
Step: 5
Therefore, graph 4 represents the given piecewise function.
Correct Answer is :   Graph 4