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

Solutions
Share 
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

Solutions
Share 
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

Solutions
Share 
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

Solutions
Share 
Step: 1
y = 1 - 2x
  [write the function.]
Step: 2
x2468
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

Solutions
Share 
Step: 1
y = 2 - 3x
  [Write the function.]
Step: 2
x481216
y = 2 - 3x  - 1.46-2.90-4- 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

Solutions
Share 
Step: 1
y = 3 - x - 2
  [Write the function.]
Step: 2
x6121824
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

Solutions
Share 
Step: 1
y = - x - 4
  [Write the function.]
Step: 2
x014
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

Solutions
Share 
Step: 1
y = x + 6
  [Write the function.]
Step: 2
x149
y = x  123
  [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

Solutions
Share 
Step: 1
y = 6 - x - 2.
  [Write the function.]
Step: 2
x6121824
y = 6 -x - 2  42.842 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

HighSchool Math