Day 1 Objective(s): Today we will identify and evaluate functions. We will differentiate between relations and functions Each day write down the objective at the top of your note page in your own words. Riddle: I’m tall when I’m young I’m short when I’m old … What am I? DEFINITIONS: Relation Definition: A rule that relates two quantities Function Definition: A relation that assigns each element “x” to exactly one element “y”. A special type of relation

Video https://youtu.be/sE4eq0cjLFk

How do we represent relations? Relations are represented in four main ways! 1. Verbally: A sentence describes how inputs and outputs are related Example: The output is 2 more than the input 2. Numerically: A table of values or a set of ordered pairs Example: (0,2), (1,3), (2, 4), (3,5) 3. Graphically: Points on a graph Example: 4. Algebraically: An equation relates the x and y coordinates of each pair Example: y = x + 2

Practice: Is it a function or NOT? 1. The input value x is a student’s ID number, and the output value y is the students score on a physics exam Answer: Yes, each x-value can only be assigned to one y-value 2. Does this table of values represent a function? Answer: Yes, each a-value has only ONE “y” x -8 -5 3 6 y -4 -3 -2

Practice – Function or Not? 3. Does this graph represent a function? Answer: No, it has more than one y value for each x value! THEOREM: Vertical Line Test A graph is a function if no two points on the graph lie on the same vertical line!

Practice – Function or Not? 4. Does this equation represent a function? Answer: No, because there will be two y-values for every x-value!

Do Now – Function or not? Determine whether the following are a function or not! 1. The input value x is the year and the output value y is the day of the week Answer: Not a function 2. Answer: No, each a-value has only ONE “y” RIDDLE: NOON good -- What does this stand for? x -8 -5 6 y -4 -3 -2

Day 2 Objective: To evaluate functions at given x-values & find the domain and range of functions!

Find Function Values – Evaluate! *REMINDER* G______________ E______________ R______________ M______________ D______________ A______________ S_______________ Find Function Values – Evaluate! If , find each function value. a. Answer: g(6) = 60 b. Answer: g(-4x) = 16x2-32x-24 c. Answer: g(5c+4) =25c2+80c+24 a. g(6) b. g(-4x) c. g(5c+4)

Domain & Range Domain: Definition: All possible inputs or “x” values Definition: All possible outputs or “y” values

Practice For the following relations state whether or not it’s a function then state its domain and range A. B.

What if I have an equation? Find the domain and range! A. B. Things to look out for when finding Domain! 1. 2.