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Understanding Relations and Functions in Math

Learn about relations and functions, and how to determine if a relation is a function or not. Practice expressing relations as tables, graphs, and mapping diagrams to understand domain and range.

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Understanding Relations and Functions in Math

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  1. Bell Work 1/20/15 Write in slope-intercept form the equation of the line passing through the given point and PERPENDICULAR to the given line.

  2. Yesterday’s Homework • Any questions? • Please pass your homework to the front. • Make sure the correct heading is on your paper. • Is your NAME on your paper? • Make sure the homework is 100% complete. • Incomplete work will NOT be accepted.

  3. Heading 1/3/2020 Relations and Functions TSWBAT: tell if a relation is a function or not. Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.

  4. Notes • Domain (the inputs) = all of the x-values of an ordered pair. • Range (the outputs) = all of the y-values of an ordered pair. • Relation = Any set of ordered pairs. • EVERYTHING is a relation. • ALL ordered pairs and ALL lines. • Function = A relation where for every input there is exactly one output. • Every function is a relation.

  5. Notes Now you try. Function or not? Ex. Ex. Ex. Ex. D R D R D R D R Function Function Not a Function Not a Function

  6. Notes Express each relation as a table, as a graph, and as a mapping diagram. What is the domain and range? Is it a function? Ex.

  7. Notes Express each relation as a table, as a graph, and as a mapping diagram. What is the domain and range? Is it a function? Ex.

  8. Notes Now you try. Express each relation as a table, as a graph, and as a mapping diagram. What is the domain and range? Is it a function? Ex.

  9. Notes • Vertical Line Test = A graph is a function if no vertical line touches more than one point. Function or not? Ex. Run a vertical line through the entire graph. Do I ever hit the graph more than once? Not a Function

  10. Notes Now you try. Function or not? Ex. Ex. Function Function

  11. Notes Now you try. Function or not? Ex. Ex. Not a Function Not a Function

  12. Summary • Everything is a _______. A function is a relation that for every input there is only ____ output. With a graph, all you have to do is use the Vertical Line ____ to determine if something is a ________. • relation • one • Test • function

  13. Ticket Out the Door • Complete the Ticket Out the Door without talking!!!!! • Talking = time after the bell! • Put your NAME on the paper. • When finished, turn your paper face DOWN. • Express each relation as a table, as a graph, and as a mapping diagram. What is the domain and range? Is it a function?

  14. Today’s Homework • Rules for Homework • Pencil ONLY. • Must show all of your work. • NO WORK = NO CREDIT • Must attempt EVERY problem. • Always check your answers.

  15. Homework 4.2 Express each relation as a table, as a graph, and as a mapping diagram. What is the domain and range? Is it a function? Function or not? 4. 5. 6.

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