#### Solved Examples and Worksheet for Identifying and Graphing Square Root Functions

Q1Identify the graph of y = - (x - 1) + 2. A. Graph 4
B. Graph 2
C. Graph 1
D. Graph 3

Step: 1
The equation y = - (x - 1) + 2 represents reflection across x axis, translation of 1 unit right and 2 units up from the graph of parent function y = (x ) shown by the graph Step: 2
Among the given graphs, graph 2 gives the above description.
Correct Answer is :   Graph 2
Q2Identify the graph that represents the square root function y = x - 2 A. Graph 4
B. Graph 2
C. Graph 3
D. Graph 1

Step: 1
y = x - 2
Step: 2
Draw y = x.
Step: 3
Make a table of values: Step: 4
Graph these points. Step: 5
The graph of y = x - 2 is obtained by shifting the graph of y = x vertically down by 2 units. Step: 6
So, graph 3 represents the square root function y = x - 2.
Correct Answer is :   Graph 3
Q3Identify the graph of the square root function y = - x - 5. A. Graph 3
B. Graph 4
C. Graph 2
D. Graph 1

Step: 1
y = - x - 5
Step: 2
Let's first draw y = -x.
Step: 3
Make a table of values: Step: 4
Graph these points. Step: 5
The graph of y = -x - 5 is obtained by shifting the graph of y = -x to the right horizontally by 5 units. Step: 6
So, graph 3 represents the square root function y = - x - 5.
Correct Answer is :   Graph 3
Q4Identify the graph of the function y = 1 - 2x. A. Graph 3
B. Graph 4
C. Graph 2
D. Graph 1

Step: 1
y = 1 - 2x
[write the function.]
Step: 2
 x 2 4 6 8 y = 1 - 2x - 1 -1.82 -2.46 -3
[Make a table of values.]
Step: 3
The graph of y = 1 - 2x is as shown.
[Plot the points from the table of values of y = 1 - 2x and join them with a smooth curve.] Correct Answer is :   Graph 1
Q5Identify the graph of the function y = 2 - 3x A. Graph 4
B. Graph 2
C. Graph 1
D. Graph 3

Step: 1
y = 2 - 3x
[Write the function.]
Step: 2
 x 4 8 12 16 y = 2 - 3x - 1.46 -2.9 -4 - 4.93
[Make a table of values.]
Step: 3
The graph of y = 2 - 3x is as shown.
[Plot the points from the table of values of y = 2 - 3x and join them with a smooth curve.] Correct Answer is :   Graph 2
Q6Identify the graph of the function y = 3 - x - 2. A. Graph 4
B. Graph 2
C. Graph 1
D. Graph 3

Step: 1
y = 3 - x - 2
[Write the function.]
Step: 2
 x 6 12 18 24 y = 3 - x -2 1 -0.16 -1 - 1.69
[Make a table of values.]
Step: 3
The graph of y = 3 - x - 2 is as shown.
[Plot the points from the table of values of y = 3 - x - 2 and join them with a smooth curve.] Correct Answer is :   Graph 3
Q7Identify the graph of the function y = - x - 4. A. Graph 2
B. Graph 3
C. Graph 1
D. Graph 4

Step: 1
y = - x - 4
[Write the function.]
Step: 2
 x 0 1 4 y = - x 0 -1 -2
[Make a table of values to draw the graph of y = - x.]
Step: 3
The graph of y = - x is as shown.
[Plot the points from the table of values of y = - x and join them with a smooth curve.] Step: 4
The graph of y = - x - 4 is obtained by shifting the graph of y = - x to the right horizontally by 4 units. Step: 5
So, graph 2 represents the square root function y = - x - 4.
Correct Answer is :   Graph 2
Q8Identify the graph of the function y = x + 6. A. Graph 4
B. Graph 2
C. Graph 3
D. Graph 1

Step: 1
y = x + 6
[Write the function.]
Step: 2
 x 1 4 9 y = x 1 2 3
[Make a table of values to draw the graph of y = x.]
Step: 3
The graph of y = x is as shown.
[Plot the points from the table of values of y = x and join them with a smooth curve.] Step: 4
The graph of y = x + 6 is obtained by shifting the graph of y = x vertically upwards by 6 units. Step: 5
So, Graph 4 represents the square root function y = x + 6.
Correct Answer is :   Graph 4
Q9Identify the graph of the function y = 6 - x - 2. A. Graph 1
B. Graph 2
C. Graph 4
D. Graph 3

Step: 1
y = 6 - x - 2.
[Write the function.]
Step: 2
 x 6 12 18 24 y = 6 -x - 2 4 2.84 2 1.31
[Make a table of values.]
Step: 3
The graph of y = 6 - x - 2 is as shown.
[Plot points from the table of values of y = 6 - x - 2 and join them with a smooth curve.] Correct Answer is :   Graph 2
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