relations and functions remediation notes
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Relations & FunctionsRemediation Notes
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VocabularyRelationDomainRangeFunctionVertical Line Test
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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!
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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}
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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}
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FunctionsHow can you tell if a relation is a function?
Mapping Domain does NOT repeat values, but
range CAN Vertical Line Test
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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.
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In Figure 1, 3 is mapped to 5
and 6…thus making this NOT A FUNCTION!
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In Figure 2, All values in the
domain are mapped to
different range values…thus
making this A FUNCTION!
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Are Figures 3 & 4 Function?
Figure 3 is a Function!
Figure 4 is NOT a Function!
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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!
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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!
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FunctionsHow can you tell if a relation is a
function?
Vertical Line Test
A Vertical line goes in an Up and Down direction.
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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
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Each graph to the right
IS A FUNCTION!
Notice the vertical line?
It is only crossing the graphs once
VERTICALLY!
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Each graph to the right IS NOT A
FUNCTION! Notice the
vertical line?It is crossing each of the
graphs more than once
VERTICALLY!
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You are now ready to begin the Remediation
Assignment
Good luck!