1. 2.1 Functions

2. Objectives: Does a relation represent a function?
From a set of ordered pairs, equations and graphs (2.2)
Evaluating functions
Operations with functions

3. A set of ordered pairs X – domain elements Y – range elements
Relation:
A set of ordered pairs
X – domain elements
Y – range elements

4. Function:
A relation in which each domain element is paired with exactly one range element

5. Is this relation a function?
{ 1,4 , 2,5 , 3,6 , 4,7 }
1,4 , 2,4 , 3,5 , 6, 10
−3,9 , −2,4 , 0,0 , 1,1 , 3,8
𝑦=2𝑥−5
𝑥 2 + 𝑦 2 =100

6. Evaluate each function: 𝑓 𝑥 =2 𝑥 2 −3𝑥
𝑓 3
𝑓 𝑥 +𝑓 3
3𝑓 𝑥
𝑓(−𝑥)
−𝑓 𝑥
𝑓 3𝑥
𝑓(𝑥+3)

7. Operations with functions
𝑓+𝑔 𝑥 =𝑓 𝑥 +𝑔 𝑥
𝑓−𝑔 𝑥 =𝑓 𝑥 −𝑔 𝑥
𝑓∙𝑔 𝑥 =𝑓 𝑥 ∙𝑔 𝑥
𝑓 𝑔 𝑥 = 𝑓(𝑥) 𝑔(𝑥) 𝑔 𝑥 ≠0
Do on board:
Given f(x) = x^2 + 9
g(x) = 3x + 5
(f+g)(x)
(f-g)(x)
(f*g)(x)
(f/g)(x)

8. Homework:
Pg. 69 #19 – 45 odd
#63– 71 odd

9. 2.1 Functions
Day 2

10. Objectives: Find the domain of a function
Evaluating a difference quotient

11. Domain:
The largest set of real numbers for which the value 𝑓(𝑥) is a real number

12. Find the domain of the following functions:
𝑓 𝑥 = 𝑥 2 +5𝑥
𝑔 𝑥 = 3𝑥 𝑥 2 −4
ℎ 𝑡 = 4−3𝑡
𝐹 𝑥 = 3𝑥+12 𝑥−5

13. Evaluate the function for the difference quotient. Simplify.
𝑓 𝑥+ℎ −𝑓(𝑥) ℎ (ℎ≠0)
𝑓 𝑥 =2𝑥 −5
𝑓 𝑥 =2 𝑥 2 −3𝑥

14. Homework:
Pg. 69 #47 – 61 odd
#75, #77