Identifying a Function Today’s Lesson: What: Identifying a Function Why: . . . so I can identify a function and become familiar with basic function vocabulary. Input Output

What are 4 ways to represent a function?

What are 2 ways to identify a function?

Let’s see what you remember What to expect in this unit . . . Up to now, you have solved equations with only one variable. In this unit, you will see a type of equation that has TWO variables– an x AND a y !! You will learn that these equations graph as a straight line. When you hear things like x . . . y . . . and graph . . . Does anything come to mind?? Think about what you learned in 6th grade. What do you think?? COORDINATE PLANE SOUND FAMILIAR?? In this unit, we will be graphing linear equations on a coordinate plane. Let’s see what you remember about plotting points!!!

Coordinate plane review: Label the following parts: origin x axis y axis Quad I Quad II Quad III Quad IV Q II y Q I F A origin E x B G D C Q III Q IV On the above coordinate plane, plot the following points: A (2, 3) B (-3,-1) C (0, -6) D (9, -5) E (-6, 0) F (-4, 6) G (4, -4)

Essential vocabulary: Ordered Pair A name we use for the x and _______ values that make up a point on the coordinate plane. y Relation A group of ordered _____________________. pairs Function A special ___________________ of relation where there is one and only one “y” value for every “x” value. (“x” can never repeat) TYPE All functions are relations, but Not all relations are functions!!!

Essential vocabulary: What is the Domain of the following relation? {(1,2); (2,3); (3, 4); (4,5)} _________________________________ 3 ways to name “x” and “y”: x y INPUT RANGE INDEPENDENT OUTPUT DOMAIN D = {1, 2, 3, 4} DEPENDENT What is the Range of the following relation? {(1,3); (2,5); (3, 7); (4,9)} _________________________________ R = {3, 5, 7, 9}

See? An equation with BOTH x and y!! 4 ways to represent a function: As an equation y = _____ 1 4x - 2 With ________ “y is equal to the product of 4 and x, minus two.” 2 WORDS See? An equation with BOTH x and y!! 3 As a _______ 4 As a table x y -2 1 2 6 3 __ GRAPH 10

How to identify a function . . . METHOD ONE: Look to see if the “x” values repeat . . . If there is more than one _______ value that is the same #, then the relation is ___________ a function! x NOT Are the following examples functions? Answer “YES” or “NO” ___________ 2) _____________ 3) ______________ YES YES NO x y 3 1 2 x y -5 5 10 15 x y -1 -2 -4 1 2 4) __________ { (-2, 0); (0, 2); (2, 0); (4, 6) } YES 5) __________ { (-2, 0); (0, 3); (-2, 2 ); (5, 7) } NO

METHOD TWO: VERTICAL LINE TEST — Look at the graph of the function. If any two points on the graph can be connected by a ________________ line, then the relation is NOT a function! vertical Are the following examples functions? Answer “YES” or “NO” ______ 2) ______ 3) ______ 4) ______ YES NO YES NO

Wrap it up/Summary: 1) What are 4 ways to represent a function? 2) What are 2 ways you can identify a function? Equations Words Table Graph -Look to see if the “x” values repeat. “x” can never repeat! -Vertical Line Test

“Is it a Function?” Worksheet Homework/ practice Due by next class! “Is it a Function?” Worksheet

END OF LESSON