Relations & FunctionsRemediation Notes

VocabularyRelationDomainRangeFunctionVertical Line Test

What is a relation? A relation is a set of ordered pairs.

{ } means set (1, 2), (-1, 3), (-2, -5) are ordered pairs

Now put this together and you have…{(1, 2), (-1, 3), (-2, -5)} a RELATION!

Everything that is a set of points is a relation…don’t let the word relation confuse you.. especially on the EOC!

Domain INPUT**The domain is the set of x values

What is the domain in the below relation? {(1, 2), (-1, 3), (-2, -5)}

Domain: {1, -1, -2}

Range OUTPUT**The range is the set of y values

What is the range in the below relation? {(1, 2), (-1, 3), (-2, -5)}

Range: {2, 3, -5}

FunctionsHow can you tell if a relation is a function?

Mapping Domain does NOT repeat values, but

range CAN Vertical Line Test

FunctionsHow can you tell if a relation is a function?

Mapping With mapping, we will check to see if every

value of x (Domain) has only one mapping to a y value.

In Figure 1, 3 is mapped to 5

and 6…thus making this NOT A FUNCTION!

In Figure 2, All values in the

domain are mapped to

different range values…thus

making this A FUNCTION!

Are Figures 3 & 4 Function?

Figure 3 is a Function!

Figure 4 is NOT a Function!

FunctionsHow can you tell if a relation is a function?

Domain does NOT repeat values

{(1, 2), (-1, 3), (-2, -5)}

Is this a Function?Do the x values repeat?

No, the x values do not repeat…thus, this IS A FUNCTION!

FunctionsHow can you tell if a relation is a function?

Domain does NOT repeat values

{(-1, 2), (-1, 3), (-2, -5)}

Is this a Function?Do the x values repeat?

Yes, the x values do repeat…thus, this IS NOT A FUNCTION!

FunctionsHow can you tell if a relation is a

function?

Vertical Line Test

A Vertical line goes in an Up and Down direction.

FunctionsHow can you tell if a relation is a

function?

Vertical Line Test

Does a vertical line cross throughthis graph more than once?

If so, then this relation (graph) is NOT a

function!Not A

FUNCTION

1

2

Each graph to the right

IS A FUNCTION!

Notice the vertical line?

It is only crossing the graphs once

VERTICALLY!

Each graph to the right IS NOT A

FUNCTION! Notice the

vertical line?It is crossing each of the

graphs more than once

VERTICALLY!

You are now ready to begin the Remediation

Assignment

Good luck!