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# Module 4 topic 1 part 3 notes

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### Module 4 topic 1 part 3 notes

1. 1. Module 4 Topic 1 The Coordinate Plane Midpoint Formula Relations & Functions (Part 3)
2. 2. <ul><li>Vocabulary </li></ul><ul><ul><li>Relation </li></ul></ul><ul><ul><li>Domain  (Independent Variable) </li></ul></ul><ul><ul><li>Range  (Dependent Variable) </li></ul></ul><ul><ul><li>Function </li></ul></ul><ul><ul><li>Vertical Line Test </li></ul></ul><ul><ul><li>Functional Notation  f(x) </li></ul></ul>
3. 3. <ul><li>What is a relation? </li></ul><ul><li>A relation is a set of ordered pairs . </li></ul><ul><li>{ }  means set </li></ul><ul><li>(1, 2), (-1, 3), (-2, -5)  are ordered pairs </li></ul><ul><li>Now put this together and you have… </li></ul><ul><li>{(1, 2), (-1, 3), (-2, -5)}  a RELATION! </li></ul>Everything that is a set of points is a relation …don’t let the word relation confuse you..especially on the EOC!
4. 4. <ul><li>Domain  is also called the Independent Variable </li></ul><ul><li>**The domain is the set of x values </li></ul><ul><li>What is the domain in the below relation? </li></ul><ul><li>{(1, 2), (-1, 3), (-2, -5)} </li></ul>Domain: {1, -1, -2}
5. 5. <ul><li>Range  is also called the Dependent Variable </li></ul><ul><li>**The range is the set of y values </li></ul><ul><li>What is the range in the below relation? </li></ul><ul><li>{(1, 2), (-1, 3), (-2, -5)} </li></ul>Range: {2, 3, -5}
6. 6. <ul><li>Functions </li></ul><ul><li>How can you tell if a relation is a function? </li></ul><ul><li>Mapping </li></ul><ul><li>Domain does NOT repeat values </li></ul><ul><li>Vertical Line Test </li></ul>
7. 7. <ul><li>Functions </li></ul><ul><li>How can you tell if a relation is a function? </li></ul><ul><li>Mapping </li></ul><ul><li>With mapping, we will check to see if every value of x (Domain) has only one mapping to a y value. </li></ul>
8. 8. In Figure 1, 3 is mapped to 5 and 6…thus making this NOT A FUNCTION !
9. 9. In Figure 2, All values in the domain are mapped to different range values…thus making this A FUNCTION!
10. 10. Are Figures 3 & 4 Function? Figure 3 is a Function! Figure 4 is NOT a Function!
11. 11. <ul><li>Functions </li></ul><ul><li>How can you tell if a relation is a function? </li></ul><ul><li>Domain does NOT repeat values </li></ul><ul><li>{(1, 2), (-1, 3), (-2, -5)} </li></ul><ul><li>Is this a Function? </li></ul><ul><li>Do the x values repeat? </li></ul><ul><li>No, the x values do not repeat…thus, this IS A FUNCTION! </li></ul>
12. 12. <ul><li>Functions </li></ul><ul><li>How can you tell if a relation is a function? </li></ul><ul><li>Domain does NOT repeat values </li></ul><ul><li>{(-1, 2), (-1, 3), (-2, -5)} </li></ul><ul><li>Is this a Function? </li></ul><ul><li>Do the x values repeat? </li></ul><ul><li>Yes, the x values do repeat…thus, this IS NOT A FUNCTION! </li></ul>
13. 13. <ul><li>Functions </li></ul><ul><li>How can you tell if a relation is a function? </li></ul><ul><li>Vertical Line Test </li></ul><ul><li>A Vertical line goes in an </li></ul><ul><li>Up and Down direction. </li></ul>
14. 14. <ul><li>Functions </li></ul><ul><li>How can you tell if a relation is a function? </li></ul><ul><li>Vertical Line Test </li></ul><ul><li>Does a vertical line cross through </li></ul><ul><li>this graph more than once? </li></ul>Not A FUNCTION 1 2 If so, then this relation (graph) is NOT a function!
15. 15. Each graph to the right IS A FUNCTION! Notice the vertical line? It is only crossing the graphs once VERTICALLY!
16. 16. Each graph to the right IS NOT A FUNCTION! Notice the vertical line? It is crossing each of the graphs more than once VERTICALLY!
17. 17. You are now ready to begin the Module 4 Topic 1 Assignments… The Coordinate Plane Midpoint Formula Relations & Functions