1. Section 3.5 Functions and Relations
Integrated Math
Section 3.5
Functions and Relations

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

3. 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

4. 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!!!

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

6. 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

8. Try these!
Pg #2,#4

10. 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).

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

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

13. 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) }

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

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

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

18. Function
Not function

20. 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}

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

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

23. Group work!
Pg 208 #70-80 even

24. 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.

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

26. 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

27. Group Work!
Pg #82-94 even

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

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