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 = - 1 2 | x | + 1.

Correct Answer is : Graph 1

Step: 1

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

Step: 1

[Original quadratic function.]

Step: 2

[Comparing with y = ax ^{2} + bx + c .]

Step: 3

The x -coordinate of the vertex = - b 2 a = 0 2 ( - 1 3 ) = 0

Step: 4

The values of y = - (x 2 3 ) + 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

Step: 1

[Original function.]

Step: 2

[Comparing with y = ax ^{2} + bx + c .]

Step: 3

The x -coordinate of the vertex = - b 2 a = - 0 2 ( - 1 ) = 0

Step: 4

The values of y = - x ^{2} + 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

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

So,

[Substitute x =0 in the equation y = 4( x ) - 1.]

Step: 4

So,

[Substitute x =0 in the equation y = 4( x ) + 2.]

Step: 5

So,

[Substitute x = 0, 1 in the equation y = 3( x ) .]

Step: 6

[Substitute x = 0, 1, 4 in the equation y = 4( x ) .]

Correct Answer is : y = 4( x )

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

Step: 1

The given graph is in two pieces.

Step: 2

The slope of the line, left to the origin is - 2 3 and the y-intercept = 0.

Step: 3

The equation of the line in the slope intercept form is given by y = m x + b .

Step: 4

Substituting the values for m = - 2 3 , b = 0, we get the line equation as,

y = - 2 3 x .

[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 = m x + 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 = - 2 3 x if x ≤ 0

y = 4 if x > 0

Correct Answer is : y = - 2 3 x if x ≤ 0

y = 4 if x > 0

Step: 1

[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

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

Step: 1

Make a table of values that includes both positive and negative x values.

- 3 | - 2 | - 1 | 0 | 1 | 2 | 3 | |

- 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

Step: 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

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

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

Step: 1

Make a table of values from the given graph that includes both positive and negative x values.

- 3 | - 2 | - 1 | 1 | 2 | 3 | |

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 |

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