FUNCTIONSLesson Two

WARM UP

1.What is the sum of the integers between and ?

2.Simplify:

3.What is the value of to the nearest tenth.

4.Find the equation of the line with a slope of -3 and going through the point (0, -2)

VOCABULARY QUIZ

1.What is the definition of a relation.

2.Explain the difference and relationship between an independent and dependent variable.

3.Complete: another term for domain is ______?

4.List two synonyms for output values.

Yesterday we looked at RELATIONS. We know that a relation is a set of ordered pairs. Today we are going to discover if these ordered pairs make a function.

We have looked at functions in our previous unit, SLOPE. Do you think you have an idea of what a function is?

A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x).

f(x)x y

Is a relation a function?•Focus on the x-coordinates, when given a relation.

If the set of ordered pairs have different x-coordinates, it IS A function

If the set of ordered pairs have same x-coordinates, it is NOT a function

•Y-coordinates have no bearing in determining functions.

Think of your input number, usually your x-coordinate, as a letter.

Think of your output number, usually your y-coordinate, as a mailbox.

Input number Output number

Can you have one letter going to two different mail boxes?

Not a FUNCTION

Determine whether this relation is a function.

{(2, 3), (3, 0), (5, 2), (4, 3)}

YES, every domain is different!

f(x)2 3

f(x)3 0

f(x)5 2

f(x)4 3

Determine whether the relation is a function.

{(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}

NO, 5 is paired with 2 numbers!

f(x)4 1

f(x)5 2

f(x)5 3

f(x)6 6

f(x)1 9

Is this relation a function?

{(1,3), (2,3), (3,3)}

{(1,3), (1,-3), (3,3)}

Sometimes it is not always easy to look at a graph and decide whether or not it is a function. Often when we try to decide if a relation is a function and we are looking at graphs, we can use the vertical line test.

What is the VERTICAL LINE TEST?

If any vertical line passes through more than one point of the graph, then that relation is not a function.

To use the vertical line test you must:

• Plot each point.

• Align your pencil vertically on the left side of your paper.

• Slide your pencil across your paper

• To pass the test, there can never be two points touching your pencil at the same time

• If there is any time where your pencil crosses two points while it is still vertical, the relation cannot be a function

• If there is only one point at any time on the pencil after sliding it across the paper, then it passes the test and the relation is a function

Which of the following are functions? Use the vertical line test to help you.

You are now going to work on two classwork assignments.

• Firstly, you will look at examples of relations and decide if they are function or non-functions.

• Secondly, you will be complete an error analysis task. You will need to spot the mistakes a student made whilst completing the worksheet. You must justify your answer.

HOMEWORK

Tonight’s homework is to complete a worksheet. You will need to decide if the relations are functions.