CH 1.2 FUNctions

I will be calling on random people to share your group’s ideas Warm Up: Talk with your partners about the following. Write your group’s answers down 1) What does the word “relation” mean to you. Give examples. 2) What is a relation in math? A rule of correspondence that connects elements from one set (usually denoted by ‘x’) with elements from a different set (usually denoted by ‘y’) *AKA a connection(relationship) between two or more items (x and y) 3) What is a function? A function is a rule of correspondence that assigns each element in one set EXACTLY one element in the second set. *AKA a relation with CERTANTY 4) How are relations and a functions related? A function IS a relation. A RELATIONSHIP is an connection between things (usually two or more concepts, objects, or people A RELATIONSHIP is an connection between things (usually two or more concepts, objects, or people) You have RELATIONSHIPS with family members, friends, boyfriends/girlfriends, co-workers, teachers, other classmates, etc. Make set notation I will be calling on random people to share your group’s ideas

Instructions were going to talk explore more about functions and when they exist. There are 4 signs around the room, one in each corner. After I read the first scenario, you will go to the corner that is true for you.

If you walked to school today, stand under A. If you rode your bike to school today, stand under B. If you drove or rode in a vehicle today, stand under C. If you got to school any other way, stand under D.

If it took you fewer than 10 minutes to get to school today, stand under B. If it took you 10 or more minutes to get to school today, stand under D.

If you’re an only child, stand under A. If you have only one other sibling, stand under B. If you have only two other siblings, stand under C. If you have three or more other siblings, stand under D.

If you’re wearing blue, stand under A. If you’re wearing red, stand under B. If you’re wearing black, stand under C. If you’re wearing white, stand under D.

If you were born in the first half of any month, stand under A. If you were born in the second half of any month, stand under B. If you were born in the first half of the year, stand under C. If you were born in the second half of the year, stand under D.

Which of the examples were functions (relationships with certainty)? Then have them discuss with partner for two minutes. Call on volunteers for guesses.

Functions vs. Not Function Transportation If you walked to school today, stand under A. If you rode your bike to school today, stand under B. If you drove or rode in a vehicle today, stand under C. If you got to school any other way, stand under D. Duration If it took you fewer than 10 minutes to get to school today, stand under B. If it took you 10 or more minutes to get to school today, stand under D. Siblings If you’re an only child, stand under A. If you have only one other sibling, stand under B. If you have only two other siblings, stand under C. If you have three or more other siblings, stand under D. Clothes If you’re wearing blue, stand under A. If you’re wearing red, stand under B. If you’re wearing black, stand under C. If you’re wearing white, stand under D. Birthday If you were born in the first half of any month, stand under A. If you were born in the second half of any month, stand under B. If you were born in the first half of the year, stand under C. If you were born in the second half of the year, stand under D. Now lets add formal language to the concepts we’ve just felt. “Mathematicians call the first three relationships ‘functions.’ Why? DRAW STUDENT EXS ON WHITEBOARD. Each element of domain must be matched with an element of range. Some elements of range may not be matched, or matched with two elements of domain Why do you think these relationships aren’t functions?” An element of the domain cannot be matched with two elements of the range.

Each element of domain must be matched with an element of range. Some elements of range may not be matched Two elements of the domain may be matched with the same range. One element of the domain cannot be matched with two elements of the range. USE WHITEBOARD STUDENT EXAMPLES So all of you are the domain and you all need a place to go Its ok if some of you did not bike to school, the options don’t need to be all used More than one of you may have used the same mode of transportation But you didn’t get to school by two of the options

Some Common ways to represent functions are…. Verbally Numerically Graphically Algebraically

“test” to visually determine if a graph is a function? Is there a quick way, or “test” to visually determine if a graph is a function? Why does it work? Yes, yes, yes, no

Write points on the board If you are looking at a graph, you can easily see if an X has more than 1 Y. Can you be in two places at once? Your timeline of your life and where you are at any given point is a function

Some of my favorite equations! Which ones are not a functions

Determine whether each relation is a function cont. y =1- x² –x + y² = 1

HW Questions Switch your hw with one other partner. Please put “CB: your name” on the top of the page. Get out the yellow “hw guidelines” half sheet of paper we looked at last class. Check that they have followed the directions. Make notes for improvements. Discuss any questions/incorrect answers and see if someone at your table knows how to solve. When you are finished, make a pile in the center of the table so I know you are ready to move on.

Let’s talk about the basic parent functions you have seen in Alg 2… 4 Color Exploration In groups, you will be given a set of cards The pink cards are the Graphs The yellow cards are the name of the function The green cards are the equation of the function The purple cards are the domain/ranges Match each pink, yellow, green, and purple card together appropriately. Most functions you should have seen before in Algebra 2. Use process of elimination if you get stuck. Once you have made all matches, discuss with your group any terms/symbols/functions that you may not know. I will be calling on random groups.

Ch 1.1 Notes: An Overview of Functions Vertex zero INCLUDE CONSTANT FUNCTION

Now that we have reviewed our basic parent functions, lets talk about a few more specific ways to describe them!

What is function notation? f(x) y-value f f(x) Or “y” x y

EX 1: Finding Domain and Range

ASK SIRI

Ex: What is the implied domain of

HW Pg 24 #1-6all, 9, 15-27odd, 54-57all, 86a/b onliny