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RF6: Domain and Range of Functions Write notes from this slide show on a clean sheet of notebook paper. The title is what you see above in red print. You will turn in the notes to the teacher.

Function X Y 2 7 3 11 4 This table represents a set of ordered pairs. The set of data is a function. 2 7 3 11 4 11 The set of all X’s is called the DOMAIN X Y X Y X Y { ( , ) , ( , ), ( , ) } D 2 3 4 R 7 11 D = { 2, 3, 4} The set of all Y’s is called the RANGE R = { 7, 11 } Mapping Diagram

Give the Domain and Range of the Function 2 3 4 7 11 Mapping Diagram 2 2 7 7 3 3 11 11 11 4 4 D = { , , } R = { , } What is the function? {( , ) , ( , ) , ( , )}

Give the Domain and Range of the Function. What is the function? 4 6 9 8 15 Mapping Diagram 4 4 8 8 6 6 15 15 15 9 9 D = { , , } R = { , } {( , ) , ( , ) , ( , )}

Look at the equation below. Y = 3X + 2 Y is the dependent variable X is the independent variable (domain) X’s go in 4 3 2 The value of Y depends on the value of X. Function X Y Y = 3X + 2 3( ) + 2 = 11 8 14 Y’s come out. (range)

FUNCTIONS X values {2,3,4} EQUATION Y = 3X + 2 Y values {8,11,14} DOMAIN X values {2,3,4} FUNCTION RULE EQUATION Y = 3X + 2 RANGE Y values {8,11,14}

Look at the equation below. If 3, 4 and 5 are put into the equation, what will come out? Y = 5X - 3 Remember: The value of Y depends on the value of X. (domain) 4 5 3 X’s go in X Y Y = 5X - 3 5( ) - 3 = 12 17 22 Y’s come out. (range)

The following slides contain a review of previous lesson(s) The following slides contain a review of previous lesson(s). You do not have to write notes for these slides, but be sure to view them.

This means that the relation is a function. Vertical - Line Test If a relation is graphed, the Vertical - Line test can be used to determine if it is a function. Is the relation to the left a function? Draw vertical lines. If ALL vertical lines intersect the relation at ONE point, then no two X values are the same. FUNCTION This means that the relation is a function.

This means that the relation is a NOT a function. Vertical - Line Test Is the relation to the left a function? Draw vertical lines. The 4th vertical line intersects the relation in 2 points. This means that two X values are the same. NOT a FUNCTION This means that the relation is a NOT a function.

Are the following functions? YES NO NO YES NO YES

End of Show Now ask for today’s classwork assignment. When finished with the assignment, staple your notes to the back of the assignment and turn it in to the teacher. The assignment is due at the end of the period today.