Bell Ringer {-5 < x < 5} Except x =0 {-5 < y < 5} Domain: Range: State the domain and range of the relation shown ow. {-5 < x < 5} Except x =0 {-5 < y < 5}

Bell Ringer Part 2 {(9,0), (-3,7),(-5,7), (-2,-10), (4,5)} Domain: _____________________ Range: ______________________

How does the domain and range change?

Domain and Range Quick Check! (10 points)

LEQ: What characteristics are needed for a relation to be a function??

“each x goes to one and only one y” What is a function? Function – A relation, whereby each input value is mapped/related to one and only one output value. In other words, for each input value, there is exactly one output value. “each x goes to one and only one y”

The x-value of 3 is assigned to both 6 and 5 as y-values! What is a function? Function : “each x goes to one and only one y” Is this relation a function? x y 6 -2 3 13 5 No! The x-value of 3 is assigned to both 6 and 5 as y-values!

The x-value of ¾ is assigned to both 3 and 5 as y-values! What is a function? Function : “each x goes to one and only one y” Is this relation a function? No! The x-value of ¾ is assigned to both 3 and 5 as y-values!

To be a function, no x-values can repeat! What is a function? To be a function, no x-values can repeat! Function : “each x goes to one and only one y” Is this relation a function? {(5,2), (3,-6), (4,1), (5,0), (5,3)} No! The x-value of 5 is assigned to 2, 0 and 3 as y-values!

Let’s look at a real world example of this… To be a function, no x-values can repeat! Let’s look at a real world example of this…

Egg to Basket Relation 1 Egg# Basket # Egg 1 2 Egg 2 3 Egg 3 4 Egg 4 1 This relation relates numbered eggs to a numbered basket. Play out the following relation in real-life. (That is, physically place egg #1 in basket #2, egg #4 in basket #1 and so on…) Was this physically possible? Is this a function (aka – do any “x”-values repeat?) Egg# Basket # Egg 1 2 Egg 2 3 Egg 3 4 Egg 4 1 Yes! Yes! It’s a function.

Egg to Basket Relation 3 Egg# Basket # Egg 1 3 Egg 2 Egg 3 1 Egg 4 4 This relation relates numbered eggs to a numbered basket. Play out the following relation in real-life. (That is, physically place egg #1 in basket #2, egg #4 in basket #1 and so on…) Was this physically possible? Is this a function (aka – do any “x”-values repeat?) Egg# Basket # Egg 1 3 Egg 2 Egg 3 1 Egg 4 4 So it was ok to have more than one of the same y-value? Yes! Yes! Yes! It’s a function.

No, egg 2 can’t be placed in baskets 3 and 4 at the same time! Egg to Basket Relation 2 This relation relates numbered eggs to a numbered basket. Play out the following relation in real-life. (That is, physically place egg #1 in basket #2, egg #4 in basket #1 and so on…) Was this physically possible? Is this a function (aka – do any “x”-values repeat?) Egg# Basket # Egg 1 1 Egg 2 3 4 Egg 3 2 No, egg 2 can’t be placed in baskets 3 and 4 at the same time! NOOOOO!!!

Try again… is this relation a function? #1 on note sheet! x y 4 5 7 6 1 2 -9 3 Yes! (no x-values repeat) Does it matter that I have two zeros for y? Nope!

Try again… is this relation a function? #2 on note sheet! x y 4 5 7 6 1 2 -9 No! (6 repeats as an x-value)

Try again… is this relation a function? {(4,2), (3,-7), (5,6), (-5,2), (-3,3)} Yes! (no x-values repeat)

Try again… is this relation a function? #3 on note sheet! {(4,2), (-5,-7), (5,6), (-5,2), (-3,3)} No! (-5 repeats as an x-value)

Try again… is this relation a function? #4 on note sheet! No! (3 repeats as an x-value, it is mapped to both b and c)

Try again… is this relation a function? Yes! (no x-values are mapped twice) Egg 2 and Egg 3 can physically both be placed in basket C.

Stop here day 1?

Bell Ringer {2,5,7,9,11,13} yes {1,2,3,4,5,6} Domain: Range: State the domain and range of the relation and determine if it is a relation. Domain: Range: Function? (yes or no) {1,2,3,4,5,6} {2,5,7,9,11,13} yes

LEQ: What characteristics are needed for a relation to be a function??

Relations in the Form of Graphs Is it a function? #5 on note sheet! PROBLEM! PROBLEM! PROBLEM! No! (many values repeat as x-values) (8,6) (-2,2) (3,4) (-2,-2) (8,-6) (3,-4)

Relations in the Form of Graphs Is it a function? Do you remember from your internet research what trick we could use to test if a graph is a function? Vertical Line Test!

Relations in the Form of Graphs Is it a function? Vertical Line Test! The Vertical Line Test tells me that if I can draw a vertical line ANY WHERE on my graph and it touches the graph in more than one place, the relation is NOT a function.

Relations in the Form of Graphs Is it a function? Yes! (passes vertical line test)

Relations in the Form of Graphs Is it a function? PROBLEM! NO! (fails vertical line test)

Relations in the Form of Graphs Is it a function? #6 on note sheet! How about now? Yes! (passes vertical line test)

Relations in the Form of Graphs Is it a function? PROBLEM! PROBLEM! NO! (fails vertical line test)

Relations in the Form of Graphs Is it a function? #7 on note sheet! Yes! (passes vertical line test)

Relations in the Form of Graphs Is it a function? Yes! (passes vertical line test)

Relations in the Form of Graphs Is it a function? #8 on note sheet! Yes! (passes vertical line test)

Relations in the Form of Graphs Is it a function? #9 on note sheet! Yes! (passes vertical line test)

Relations in the Form of Graphs Is it a function? Yes! (passes vertical line test)

Relations in the Form of Graphs Is it a function? #10 on note sheet! PROBLEM! PROBLEM! PROBLEM! NO! (fails vertical line test)

Relations in the Form of Graphs Is it a function? Yes! (passes vertical line test)

Relations in the Form of Graphs Is it a function? #11 on note sheet! Yes! (passes vertical line test)

Relations in the Form of Graphs Is it a function? #12 on note sheet! How about now? PROBLEM! NO! (fails vertical line test)

Relations in the Form of Graphs Is it a function? PROBLEM! No! (fails vertical line test)

Team Huddle Get out your Domain and Range Notes 1, 2 and 3 from last week. Go through each example on the note sheet and circle the graph IF IT IS A FUNCTION. Do not circle it if it is not a function.

Summarizer… Create a relation Exchange with a partner Decide if you partner’s relation is a function Exchange papers and check each other’s work