#### Solved Examples and Worksheet for Identifying Functions

Q1Which of the graphs represents the function y = - 12| x | + 1? A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

Step: 1
Make a table for different values of x as shown below.
Step: 2
Draw a graph using the tabulated values as shown below.
Step: 3
So, Graph 1 represents the function y = - 12| x | + 1.
Correct Answer is :   Graph 1
Q2Choose a graph for the equation - y = x - 2. A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

Step: 1
Choose values for x. Step: 2
Plot the points on a graph. Step: 3
The above graph matches with the Graph 2.
Step: 4
So, Graph 2 is the correct answer.
Correct Answer is :   Graph 2
Q3Choose a graph that represents the equation y = - 2x3  + 2. A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4

Step: 1
y = - 2x3 + 2
Step: 2
3y = - 2x + 6
[Multiply with 3 on both sides.]
Step: 3
Choose values for x Step: 4
Plot the points on a graph. Step: 5
The above graph matches with the graph in choice B.
Step: 6
So, choice B is the correct answer.
Correct Answer is :   Graph 2
Q4Which of the graphs best suits the quadratic function?
y = - x23 + 2 A. Graph 2
B. Graph 4
C. Graph 3
D. Graph 1

Step: 1
y = - x23+ 2
Step: 2
a = - 13, b = 0 and c = 2
[Comparing with y = ax2 + bx + c.]
Step: 3
The x-coordinate of the vertex = - b2a = 02(-13) = 0
Step: 4
The values of y = - (x23) + 2 for the x-values to the left and right of x = 0 are: Step: 5
The graph 2 satisfies the above table.
Correct Answer is :   Graph 2
Q5Identify the basic absolute value function from the graphs. A. Graph 4
B. Graph 5
C. Graph 2
D. Graph 3
E. Graph 1

Step: 1
The absolute value function is f(x) = | x |
Step: 2
Graph 3 represents the absolute value function.
Correct Answer is :   Graph 3
Q6Which is the graph of the quadratic function y = - x2 + 3? A. Graph 2
B. Graph 1
C. Graph 3
D. Graph 4

Step: 1
y = - x2 + 3
[Original function.]
Step: 2
a = - 1, b = 0, and c = 3
[Comparing with y = ax2 + bx + c.]
Step: 3
The x-coordinate of the vertex = - b2a = - 02(- 1) = 0
Step: 4
The values of y = - x2 + 3 for the x-values to the left and right of x = 0 are tabulated below: Step: 5
Plot the points and join them with a smooth curve as shown. Step: 6
The graph matches with Graph 3.
Correct Answer is :   Graph 3
Q7Identify the equation of the graph obtained when the graph of y = x2 is reflected over the x-axis.

A. y = -x + 2
B. y = -x2
C. y = -x4
D. y = -x - 2

Q8Which equation represents the graph shown? A. y = 4(x) + 2
B. y = 3(x)
C. y = 4(x) - 1
D. y = 4(x)

Step: 1
From the graph (0,0), (1,4), and (4,8) lies on the curve.
Step: 2
Substitute the points in the given equations and verify.
Step: 3
y = 4(0) - 1 = - 1 ≠ 0
So, y = 4(x) - 1 does not represent the graph.
[Substitute x =0 in the equation y = 4(x) - 1.]
Step: 4
y = 4(0)+ 2 = 2 ≠ 0
So, y = 4(x) + 2 does not represent the graph.
[Substitute x =0 in the equation y = 4(x) + 2.]
Step: 5
y = 3(0) = 0
y = 3(1) = 3≠ 4
So, y = 3(x) does not represent the graph.
[Substitute x = 0, 1 in the equation y = 3(x).]
Step: 6
y = 4(0) = 0
y = 4(1) = 4
y = 4(4) = 8. So, y = 4(x) equation represent the graph.
[Substitute x = 0, 1, 4 in the equation y = 4(x).]
Correct Answer is :   y = 4(x)
Q9Which of the graphs does not represents a step function? A. Graph 3
B. Graph 4
C. Graph 1 and Graph 2
D. Graph 1, Graph 2, and Graph 4

Step: 1
A step function is a special type of function whose graph is a series of line segments.
Step: 2
Among the graphs, Graph 3 has a series of line segments.
Step: 3
So, Graph 1, Graph 2 and Graph 4 does not represents a step function.
Correct Answer is :   Graph 1, Graph 2, and Graph 4
Q10Identify the equations for the given graph. A. y = 23 x if x ≤ 0
y = 4 if x > 0
B. y = - 23x if x ≤ 0
y = 4 if x ≥ 0
C. y = - 23x if x ≤ 0
D. y = - 23x if x ≤ 0
y = 4 if x > 0

Step: 1
The given graph is in two pieces.
Step: 2
The slope of the line, left to the origin is - 23 and the y-intercept = 0.
Step: 3
The equation of the line in the slope intercept form is given by y = mx + b.
Step: 4
Substituting the values for m = - 23, b = 0, we get the line equation as,
y = - 23x.
[The solid dot at the origin indicates y = 0 when x = 0.]
Step: 5
The slope of the line to the right of the origin is 0 and the y-intercept is 4.
Step: 6
Substitute the values of m = 0 and b = 4 in the equation y = mx + b to get,
y = 4.
[The open circle on the second piece indicates the graph begins when x > 0.]
Step: 7
Therefore, the graph represents the function,
y = - 23x if x ≤ 0
y = 4 if x > 0
Correct Answer is :   y = - 23x if x ≤ 0
y = 4 if x > 0
Q11Which graph represents the equation y = 2x + 8? A. Graph 3
B. Graph 1
C. Graph 4
D. Graph 2

Step: 1
y = 2x + 8
[Given equation.]
Step: 2
From the equation y = 2x + 8, slope is 2 and y-intercept is 8.
Step: 3
Plot the point (0, b) when b = 8.
Step: 4
Use the slope to locate a second point on line.
Step: 5
m = 21 = riserun = move 2 unit upmove 1 units right
Step: 6
Draw a line through the two points. Step: 7
The graph of the equation y = 2x + 8 matches with Graph 3.
Correct Answer is :   Graph 3
Q12Which graph represents the equation y = -|x - 4|? A. Graph 3
B. Graph 1
C. Graph 4
D. Graph 2

Step: 1
Make a table of values that includes both positive and negative x values.
 x - 3 - 2 - 1 0 1 2 3 y - 7 - 6 - 5 - 4 - 3 - 2 - 1
Step: 2
Graph the ordered pairs in the table shown and connect the points with a smooth curve.
Step: 3
Then the graph obtained matches with Graph 2.
Step: 4
So, Graph 2 represents the equation y = - |x - 4|.
Correct Answer is :   Graph 2
Q13Choose the graph for the relation shown.
f(x) = |x| + 2 when x < 1
x2 + x when x ≥ 1 A. Graph 4
B. Graph 2
C. Graph 1
D. Graph 3

Step: 1
f(x) = |x| + 2 when x < 1
x2 + x when x ≥ 1
[Given.]
Step: 2
|x| + 2 is an absolute value function.
Step: 3
When x < 1, the value of the function can be any real number.
Step: 4
x2 + x is a quadratic equation.
Step: 5
When x ≥ 1, the value of the function is greater than or equal to 2.
Step: 6
So, we can observe that Graph 2 represents the given relation.
Correct Answer is :   Graph 2
Q14Identify the graph for the function shown.
f(x) = - 2 if x ≤ 0
x - 1 if 0 < x ≤ 3
x + 1 if x > 3 A. Graph 1
B. Graph 2
C. Graph 4
D. Graph 3

Step: 1
Identify the graph for the function shown.
f(x) = - 2 if x ≤ 0
x - 1 if 0 < x ≤ 3
x + 1 if x > 3
[Given.]
Step: 2
When x ≤ 0, the value of the function remains constant at - 2.
Step: 3
When 0 < x ≤ 3, the value of the function is (- 1, 2].
Step: 4
When x > 3, the value of the function is (4, ∞).
Step: 5
So, we can observe that the Graph 1 represents the given function.
Correct Answer is :   Graph 1
Q15Choose the function which represents the given graph. A. y = - |3x |
B. y = |2x |
C. y = - |3x |
D. y = |3x |

Step: 1
Make a table of values from the given graph that includes both positive and negative x values.
 x - 3 - 2 - 1 1 2 3 y 9 6 3 3 6 9
Step: 2
From the given choices, y = |3x | satisfies the values given in above table.
Step: 3
So, the equation y = |3x | represents the given graph.
Correct Answer is :   y = |3x |