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2.01 Definitions

Worksheet
Independent and dependent variables
1

For each of the following pairs of variables:

i

State the independent variable.

ii

State the dependent variable.

a

Number of ice cream cones sold and temperature outside.

b

Size of a pizza and cost of a pizza.

c

Time spent studying and exam mark.

2

Consider the function y=4x-3. Identify the following:

a

The independent variable

b

The dependent variable

Functions vs relations
3

State whether the following statements about functions are true or false:

a

When working with a function, substituting a certain value of x into the formula gives only 1 value of y for that value of x.

b

A horizontal line can intersect the graph of a function at more than one point.

c

A relation always passes the vertical line test.

d

All functions are relations.

e

All relations are functions.

4

Are all straight lines functions? Explain your answer.

5

Determine whether the following relations are functions:

a
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
b
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
c
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
d
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
e
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
f
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
g
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
h
-6
-4
-2
2
4
6
x
-6
-4
-2
2
4
6
y
i
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
j
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
6

Determine whether the following sets of points describe a function:

a

\left\{\left(2, 5\right), \left(7, - 3 \right), \left(5, 2\right), \left( - 4 , - 9 \right)\right\}

b

\left\{\left(2, 5\right), \left(2, 7\right), \left( - 3 , - 4 \right), \left( - 9 , 13\right)\right\}

7

Find a value of k such that the relation \left\{\left(6, 2\right), \left(8, 5\right), \left(1, 7\right), \left(k, 4\right)\right\} does not represent a function.

8

The pairs of values in the following tables represent a relation between x and y. Determine whether they represent a function:

a
x-4- 3- 2-101234
y- 4- 3- 2-10-1- 2- 3- 4
b
x0148912161820
y0122 \sqrt{2}32 \sqrt{3}43 \sqrt{2}2 \sqrt{5}
c
x- 9- 7- 6- 5- 3- 23510
y101010101010101010
9

Consider the number of quarters in x years.

a

Complete the table:

b

Is this relation a function?

\text{Years, }x\text{Quarters}
1
2
3
4
5
Types of functions and relations
10

For each of the following graphs, state the type of relation it is from the following:

  • One-to-one

  • Many-to-one

  • One-to-many

  • Many-to-many

a
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
b
-8
-6
-4
-2
2
4
6
8
x
2
4
6
8
10
12
14
16
18
y
c
-4
-3
-2
-1
1
2
3
4
x
-7
-6
-5
-4
-3
-2
-1
1
y
d
-4
-3
-2
-1
1
2
3
4
x
-1
1
2
3
4
5
6
7
y
e
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
f
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
11
a

Complete the statement: "A one-to-one function is a function in which ..."

b

Is a horizontal line a one-to-one function? Explain your answer.

12

A relation is defined as: y = 1 if x is positive and y = -1 if x is 0 or negative.

a

Complete the table for this relation:

x-4 -3-2-101234
y
b

Plot the points on the number plane.

c

Do these values represent a function?

13

Consider the following ordered pairs:

\left\{\left( - 9 , - 5 \right), \left( - 5 , - 10 \right), \left( - 5 , - 4 \right), \left( - 3 , 7\right), \left( - 2 , - 4 \right), \left( - 1 , 1\right)\right\}

a

Plot the ordered pairs on the number plane.

b

Which ordered pair would need to be removed from the set so that the remaining ordered pairs represent a function?

14

Determine if the following graphs are one-to-one functions:

a
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
b
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
c
-6
-5
-4
-3
-2
-1
1
2
x
-3
-2
-1
1
2
3
4
5
y
d
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
e
-8
-7
-6
-5
-4
-3
-2
-1
1
2
x
-4
-3
-2
-1
1
2
3
4
y
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MA11-1

uses algebraic and graphical techniques to solve, and where appropriate, compare alternative solutions to problems

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