Relations and Functions

By Mr. Madison H.

    Welcome to the fun and exciting world of Relations and Functions. I am sure you are sitting there say "man what the heck are relations and functions and all those other silly terms that go along with them." Well let me help you out by telling you some of those important terms!

IMPORTANT TERMS TO REMEMBER~

• Ordered Pairs is when you group data from two groups together, such as year and population from things such as a table.                           Example: (1460, 0.4), (1470, 0.7), (1480, 1.2)....

• X-axis is the axis running horizontal on a graph.

• Y-axis is the axis running vertically on a graph.

• Origin is the point of (0,0) on a graph, where the X and Y axis intersect.

• Quadrants are the 4 areas of a graph. Quadrant 1 is positive X axis and positive Y axis. Quadrant 2 is negative X and positive Y. Quadrant 3 is negative X and negative Y. Quadrant 4 is positive X and negative Y.

• Relation is a set of ordered pairs.
  

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• Domain is the X coordinate in a set of ordered pairs or a relation.

• Range is the Y coordinate or second coordinate in a relation.

• Function is a special type of relation in which each element of the domain is paired with only one element from the range. An example of a function would be when (-2,3) (3,5) (2,6). This is a function because each domain matches with a range.

*HINT*~ To test and see if a function is a function on a graph, you can use the line test. Use a pencil and slide from left to right one time slowly. If you hit two points at the same time then it is not a function.

     TEST PROBLEM~

          Mr. Big Dirty L of Raleigh has been overwhelmed with his endless number of good looking dates each weekend. Form a table and a graph from the following information and determine whether or not it is a function.

Weekend One Mr. L had 4 offers for dates. Weekend Two Mr. L had a good week and had 9 offers for dates. Weekend Three Mr. L was sick for a few days and only had 2 offers. Weekend Four Mr. L had an average week and was offered 5 dates.  Finally on Weekend Five Mr. L blew the school away with suave ways and was offered 14 dates.      

After making the graph by placing the one of the categories along the bottom and one along the side and plotting the information you can then do the line test to figure out if this problem is a function or not.

 Mr. Big Dirty L can now see multiple things from the graph and from the table. Not only can you tell that it is a function but Mr. L can then begin to see how he needs to balance his dates in a better way and make sure he does not become over booked or stressed with good looking dates. He can also make sure to not overbook dates and see if his stud ness is dropping or rising each month. 

This chapter should not be very difficult if you work on memorizing the terms and practice graphing. The line test is a great way to fall back on if you need to decide whether the information given is a function. Work hard and do not get lazy in making your table and graphs. Have fun and good luck to all you ladies that are on Mr. Big Dirty L's list.

Inspirational Quote

People are like stained-glass windows.
They sparkle and shine when the sun is out,
but when the darkness sets in,
their true beauty is revealed only if there is a light from within.
Elizabeth Kübler-Ross

This quote from Inspirationalquotes.com is a good example of Honesty and being true to yourself. This is describing what your personality truly is and how we must be true to ourselves and let our goodness shine through even during dark and rough times.

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