Relations and Functions Explained: Domain, Range, Vertical Line Test

What is a Relation? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Domain and Range ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

For Example, ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

What is a Function? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Using the Vertical Line Test ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],……… .

Examples of the Vertical Line Test function function Not a function Not a function ……… .

Mappings ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example of a Mapping ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],-3 0 3 6 1 2 3 4 This relation is a function because each x-value maps to only one y-value. ……… .

Another Mapping ,[object Object],[object Object],-1 1 5 6 2 3 8 Notice that even though there are two 2’s in the range, you only list the 2 once. This relation is a function because each x-value maps to only one y-value. It is still a function if two x-values go to the same y-value. ……… .

Last Mapping ,[object Object],[object Object],-4 5 3 -1 0 1 9 This relation is NOT a function because the (-4) maps to the (-1) & the (0). It is NOT a function if one x-value go to two different y-values. ……… . Make sure to list the (-4) only once!

Vocabulary Review ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Practice (you will need to hit the spacebar to pull up the next slide) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Answers (you will need to hit the spacebar to pull up the next slide) ,[object Object],[object Object],[object Object],[object Object],Function Not a Function Function Not a Function -4 -2 3 4 -1 2 1 0 1 7 -6 2 -4 4

One more thing… ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

How to Evaluate a Function Rule ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],y= x + 5 y= 2x -1 y= -x + 2 y=(2)+ 5 y= 7 y=2(2)-1 y= 4 – 1 y= 3 y=-(2)+2 y= -2 + 2 y= 0 ……… .

Evaluating for a given domain ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

One more example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],……… .

Practice (you’ll need to hit the spacebar to pull up the next slide) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Answers 1. 2. y = 3x + 1 y = 3(-4) + 1 y = -12 + 1 y = -11 y = 3x + 1 y = 3(0) + 1 y = 0 + 1 y = 1 Ans. { -11, 1, 7} y = 3x + 1 y = 3(2) + 1 y = 6 + 1 y = 7 y = -2x + 3 y = -2(-5) + 3 y = 10 + 3 y = 13 y = -2x + 3 y = -2(-2) + 3 y = 4 +3 y = 7 Ans. { 13, 7, -9} y = -2x + 3 y = -2(6) + 3 y = -12 +3 y = -9

Relations and Functions Explained: Domain, Range, Vertical Line Test

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