Relations and Functions Worksheet

**Page 1**

1.

A relation is observed between the number of days of preparation by a student for math, science and statistics tests and the points he scored. The relation is: {(3, 70), (4, 90), (2, 52)}. Determine if this relation is a function or not.

a. | yes | ||

b. | no |

A relation is a function if each input corresponds to one and only one output.

So, the given relation is a function.

Correct answer : (1)

2.

Determine whether the relation {($x$, $y$): $x$ = 10} is a function.

a. | yes | ||

b. | no |

{(

That is, {_ _ _ _ (10, - 1), (10, 0), (10, 1), (10, 2), (10, 3) _ _ _ _ _ _}.

A relation is a function if each value of

So, the given relation is not a function.

Correct answer : (2)

3.

Find the domain and range of the relation graphed.

a. | domain = {3, 0, 4, 2}; range = {0, 1, 2, - 2, - 3} | ||

b. | domain = {0, 1, 2, - 2, - 3}; range = {3, 0, 4, 2} | ||

c. | domain = {2, 4}; range = {- 3, 2} | ||

d. | domain = {1,- 2}; range = {3} |

The domain of a relation is the set of all the first coordinates of the ordered pairs. The range of a relation is the set of all the second coordinates of the ordered pairs.

The domain is {0, 1, 2, - 2, - 3}.

The range is {3, 0, 4, 2}.

Correct answer : (2)

4.

Determine whether the relation graphed is a function or not.

a. | yes | ||

b. | no |

But in the graph,

So, it is not a function.

Correct answer : (2)

5.

Draw the mapping diagram for the relation and determine whether it is a function or not.

{(2, 4), (- 8, 0), (1, 5), (3, 1)}

a. | Figure 1, Relation is a function | ||

b. | Figure 3, Relation is a function | ||

c. | Figure 4, Relation is not a function | ||

d. | Figure 2, Relation is not a function |

Draw the mapping diagram for the given relation.

A relation is a function if each element in the domain is paired with one and only one element in the range.

From the mapping diagram, it can be observed that the given relation is a function.

Correct answer : (1)

6.

In the relation {($x$, $y$): $x$ = 12$y$²}, is $x$ a function of $y$?

a. | No | ||

b. | Yes |

A relation is a function if each value of

But here for two outputs, we have the same input.

For example: For

So, it is not a function.

Correct answer : (1)

7.

Identify a rule for the relation {(- 3, 33), (- 2, 22), (0, 0), (2, 22), (3, 33)}.

a. | {($x$, $y$): $y$ = - | 11$x$ |, $x$ = - 3, - 2, 0, 2, 3} | ||

b. | {($x$, $y$): $y$ = - 11$x$, $x$ = - 3, - 2, 0, 2, 3} | ||

c. | {($x$, $y$): $y$ = 11$x$, $x$ = - 3, - 2, 0, 2, 3} | ||

d. | {($x$, $y$): $y$ = | 11$x$ |, $x$ = - 3, - 2, 0, 2, 3} |

From the given relation, it can be observed that the

So, the relation is: {(

Correct answer : (4)

8.

Laura is building rectangular boxes of different sizes. The length of the box '$y$' is 8 times its width '$x$'. If the widths she is using are 5 cm, 7 cm and 9 cm, then choose a rule for the relation between the length and the width and determine if this relation is a function.

a. | {($x$, $y$): $x$ = 8$y$, $x$ = 5, 7, 9}, not a function | ||

b. | {($x$, $y$): $x$ = 8$y$, $x$ = 5, 7, 9}, function | ||

c. | {($x$, $y$): $y$ = 8$x$, $x$ = 5, 7, 9}, function | ||

d. | {($x$, $y$): $y$ = 8$x$, $x$ = 5, 7, 9}, not a function |

Width of the box =

The relation is: {(

The Ã¢â‚¬Ëœ

The ordered pairs are (5, 40), (7, 56), (9, 72)

A relation is a function if each value of

So, the given relation is a function.

Correct answer : (3)

9.

Evaluate 6$f$(10), if $f$($x$) = 10$x$² + 6$x$ - 4.

a. | 6336 | ||

b. | 1056 | ||

c. | 10640 | ||

d. | 1064 |

[Replace

[Simplify.]

Therefore, 6

[Simplify.]

Correct answer : (1)

10.

Evaluate $g$(3$x$) + $h$(- 10), if $g$($x$) = - 8$x$ + 16 and $h$($x$)= 5$x$² + 2$x$ + 8.

a. | - 24$x$ - 504 | ||

b. | - 24$x$ + 504 | ||

c. | 24$x$ - 504 | ||

d. | 24$x$ + 504 |

[Replace

= - 24

[Replace

= 500 - 20 + 8

[simplify.]

Correct answer : (2)