Solved Examples and Worksheet for Graphing Linear Functions for a Given Domain

Q1Find the solution set for y = x - 12, given the replacement set {(- 4, - 92), (- 3, - 72), (3, 72), (6, 132)}.
A. {(- 4, - 92), (- 3, - 72), (3, 72)}
B. {(- 3, - 72), (3, 72)}
C. {(3, 72), (6, 132)}
D. {(- 4, - 92), (- 3, - 72)}

Solutions
Share 
Step: 1
Make a table. Substitute each ordered pair into the equation.
Step: 2
The ordered pairs (- 4, - 92) and (- 3, - 72) result in true statement.
Step: 3
The solution set is {(- 4, - 92), (- 3, - 72)}.
Correct Answer is :   {(- 4, - 92), (- 3, - 72)}
Q2Find the solution set for y = 13x, given the replacement set {(- 32, - 12), (- 1, - 23), (- 12, - 16), (0, 0), (8, 92)}.

A. {(- 12, - 16) , (0, 0), (8, 92)}
B. {(- 1 , - 23), (0, 0), (8, 92)}
C. {(0, 0), (8 , 92)}
D. {(- 32, - 12), (- 12, - 16), (0, 0)}

Solutions
Share 
Q3Find the solution set for b = a + 12, if the domain is {12, 32, 52, 72}.

A. {1, 2, 3, 4}
B. {(1, 12), (2, 32), (3, 52), (4, 72)}
C. {(12, 1), (32, 3), (52, 5), (72, 7)}
D. {(12, 1), (32, 2), (52, 3), (72, 4)}

Solutions
Share 
Step: 1
Make a table. The values of a come from the domain. Substitute each value of a into the equation to determine the values of b in the range.
Step: 2
The solution set is {(12, 1), (32, 2), (52, 3), (72, 4)}.
Correct Answer is :   {(12, 1), (32, 2), (52, 3), (72, 4)}
Q4Solve y = x + 8 if the domain is {2, 3, 4, 5}. Graph the solution set.

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

Solutions
Share 
Step: 1
Make a table. The values of x come from the domain. Substitute each value of x into the equation to determine the values of y in the range.
Step: 2

Step: 3
The solution set is {(2, 10) (3, 11) (4, 12) (5, 13)}.
Step: 4
The graph that represents the solution set is Graph 1.
Correct Answer is :   Graph 1
Q5Solve y = x + 10 if the domain is {- 3, - 2, 0, 4}. Graph the solution set.

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

Solutions
Share 
Step: 1
Make a table. The values of x come from the domain. Substitute each value of x into the equation to determine the values of y in the range.
Step: 2

Step: 3
The solution set is {(- 3, 7), (- 2, 8), (0, 10), (4, 14) }.
Step: 4
The graph that represents the solution set is Graph 2.
Correct Answer is :   Graph 2
Q6Solve y = 3x - 4 if the domain is {2, 4, 6, 8}. Graph the solution set.

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

Solutions
Share 
Step: 1
Make a table. The values of x come from the domain. Substitute each value of x into the equation to determine the values of y in the range.
Step: 2
The solution set is {(2, 2), (4, 8), (6, 14), (8, 20) }.
Step: 3
The graph that represents the solution set is Graph 3.
Correct Answer is :   Graph 3
Q7Solve x = 12 - y if the domain is {1,3,7,8} . Graph the solution set.

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

Solutions
Share 
Step: 1
x = 12 - y
  [Original equation.]
Step: 2
y = 12 - x
  [Reframe the equation.]
Step: 3
Make a table. The values of x come from the domain. Substitute each value of x into the equation to determine the values of y in the range.
Step: 4

Step: 5
The graph that represents the solution set is Graph 2.
Correct Answer is :   Graph 2
Q8Graph the solution set for x + 5y = 25, if the domain is {5 ,10,15,20}

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

Solutions
Share 
Step: 1
x + 5y = 25
  [Original Equation]
Step: 2
Substitute each value of x from the domain to determine the corresponding values of y in the range.
Step: 3
The graph that represents the solution set is Graph 4.
Step: 4
So, the correct choice is Graph 4.
Correct Answer is :   Graph 4
Q9Solve 2x = y - 10 if the domain is {1, 2, 3, 4} . Graph the solution set.


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

Solutions
Share 
Step: 1
2x = y - 10
  [Original Equation]
Step: 2
Substitute each value of x from the domain to determine the corresponding values of y in the range.
Step: 3
The graph that represents the solution set is Graph 2.
Correct Answer is :   Graph 2
Q10Graph the solution set for x + y2 = 10, if the domain is { 2, 4, 6, 8}

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

Solutions
Share 
Step: 1
x + y2 = 10
  [Given equation.]
Step: 2
Substitute each value of x from the domain to determine the corresponding values of y in the range
Step: 3
So, the correct choice is Graph 2.
Correct Answer is :   Graph 2
Q11Solve y = x if the domain is {- 3, - 2, 0, 4}. Graph the solution set.

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

Solutions
Share 
Step: 1
Make a table. The values of x come from the domain. Substitute each value of x into the equation to determine the values of y in the range.
Step: 2

Step: 3
The solution set is {(- 3, -3), (- 2, -2), (0, 0), (4, 4) }.
Step: 4
The graph that represents the solution set is Graph 4.
Correct Answer is :   Graph 4
Q12Graph the solution set for y = - x + 10, if the domain is { - 2, - 1, 0, 1, 2}


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

Solutions
Share 
Step: 1
y = - x + 10
  [Given equation.]
Step: 2
Substitute each value of x from the domain to determine the corresponding values of y in the range
Step: 3
So, the correct choice is Graph 2.
Correct Answer is :   Graph 2
Q13Solve y = x + 5 if the domain is {-2, -1, 1, 3}. Graph the solution set.


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

Solutions
Share 
Step: 1
Make a table. The values of x come from the domain. Substitute each value of x into the equation to determine the values of y in the range.
Step: 2

Step: 3
The solution set is {(-2, 3), (-1, 4), (1, 6), (3, 8)}.
Step: 4
The graph that represents the solution set is Graph 1 as shown below.
Correct Answer is :   Graph 1
Q14Solve y = x - 3 if the domain is { -3, -1, 1, 2, 5 }. Graph the solution set.

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

Solutions
Share 
Step: 1
Make a table. The values of x come from the domain. Substitute each value of x into the equation to determine the values of y in the range.
Step: 2
The solution set is {(-3, -6), (-1, -4), (1, -2), (2, -1), (5, 2)}.
Step: 3
The graph that represents the solution set is Graph 2 as shown below.
Correct Answer is :   Graph 2
Q15Solve x = 9 - y if the domain is {3, 8, 9, 10}. Graph the solution set.


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

Solutions
Share 
Step: 1
x = 9 - y
  [Original equation.]
Step: 2
y = 9 - x
  [Reframe the equation.]
Step: 3
Make a table. The values of x come from the domain. Substitute each value of x into the equation to determine the values of y in the range.
Step: 4
The solution set is {(3, 6), (8, 1), (9, 0), (10, -1)}.
Step: 5
The graph that represents the solution set is Graph 1 as shown below.
Correct Answer is :   Graph 1

HighSchool Math