Section 3.5 Functions and Relations Integrated Math Section 3.5 Functions and Relations

Recall the definitions for a linear function, independent variable and dependent variable.

y is a function of x means there is a rule that determines y values (dependent variable) when given an x-value (independent variable) Function-rule where every x-value has a unique y-value

You might put two different numbers in and get the same y coming out You will NEVER put a number (x) in a function and get two numbers (y) out!!!

There will never be two or more y’s paired with one x. Two different x’s can be paired with the same y.

Which would be a function? Scenario #1 Let x= student school ID number Let y= student’s last score on a math test Scenario #2 Let x= a test score Let y=student ID numbers with a given score

http://www.youtube.com/watch?v=sE4eq0cjLFk

Try these! Pg. 206 #2,#4

http://www.youtube.com/watch?v=ilhbOietyqA

Writing a function A phone plan costs $15.00 plus 10¢ per text. Write a function expressing the monthly cost (C) as a function of the number of text messages (t).

Functions Expressed as Tables What is the function rule? x y 4 6 8 12 14 20 22 26 28

Relation-any set of ordered pairs. A function is a special type of relation.

When given a set of ordered pairs, the relation is a function if no x value is repeated with different y’s. #1 { (4,6) (2,8) (2,5) } #2 { (7,3) (7,1) (12,15) } #3 { (6,5) (8,5) (10,17) }

https://www.youtube.com/watch?v=VUTXsPFx-qQ

Assignment #15A Pg. 206 #1-33 odd

When you look at a graph if any vertical line crosses more than one point, you don’t have a function!

Function Check Vertical line test- if a vertical line goes through more than one point on a graph, the graph is not a function.

Function Not function

Domain- set of input (x) values (independent) Range- set of output (y) values (dependent) For ordered pairs- {(2,8) (3,9) (4,10) (5,10)} Domain {2,3,4,5} Range {8,9,10}

For all linear equations that can be written in the form y=mx+b Domain Ɍ Range Ɍ Vertical lines are not functions!!!!!!!

Square root functions-the expression under the radical must be ≥0 and the square root value must be ≥0 𝑦= 𝑥−10 Domain? Range?

Group work! Pg 208 #70-80 even

Function notation Read f(x) as “f of x” y= 2x+5 can be written as f(x)=2x+5 When there is a number in the parentheses, you are given the input value f(3) is asking for the output value when 3 is the input value.

f(x) = 4x-5 x⟶ ⟶𝑦 f(3) = ? f(1) = ? f(-6) = ? f(0) = ?

f(x) = 4x-5 f(3) = 4(3)-5=7 f(1) = 4(1)-5=-1 f(-6) = 4(-6)-5=-29 f(0) = 4(0)-5=-5

Group Work! Pg. 208 #82-94 even

Look at #102 on page 208 Two steps #1 Write a function #2 Find P(40)

Assignment #15B Pg. 207 #63-79 odd, #81-103 odd