1. Bell work: Which of these are ways to represent a function? f(x)=x+3
(0,1),(1,2),(2,3),(3,4),(4,5)…
Double a number and add six
The image to the right

2. What is a function?
In your groups, arrive at a shared definition of what a ‘function’ is. When you’re finished, turn in your group’s definition(with all member’s names)
We will discuss different definitions as a class.

3. 1.1: Functions and Relations

4. Function, relation, or neither?

5. Function, relation, or neither?

6. Relations vs functions
A relation is some relationship between inputs and outputs
A function is a relation that matches each input WITH ONLY ONE output

7. Is this a function?

8. Which are not functions?

9. Domain and Range Domain is the set of all inputs(aka x-values)
Range is the set of all outputs (aka y-values)

10. What is the domain and range of these functions?
f(x) = 5x+7
g(x) = 5 𝑥 2
h(x) = 17 𝑥 2 −9
r(x) = 𝑥−100

11. 1.2: Composition of Functions

12. What is a composition of functions?

13. Adding functions
If f(x)= 𝑥 2 +5, and g(x) = x + 7, what is f(4) + g(4) ?
If h(x)= 𝑥 2 +𝑥+12, what is h(4) ?

14. Adding functions
If f(x)= 𝑥 3 -2, and g(x) = 𝑥−2 , what is f(2) + g(2) ?
If h(x)= 𝑥 𝑥−2 , what is h(2) ?

15. Subtracting functions
If f(x)= 𝑥 2 +5, and g(x) = x + 7, what is f(4) - g(4) ?
If f(x)= 𝑥 3 -2, and g(x) = 𝑥−2 , what is f(2) - g(2) ?

16. Multiplying functions
If f(x)= 𝑥 2 +5, and g(x) = x + 7, what is f(4) * g(4) ?
If f(x)= 𝑥 3 -2, and g(x) = 𝑥−2 , what is f(2) * g(2) ?

17. Dividing functions
If f(x)= 𝑥 2 +5, and g(x) = x + 7, what is f(4) / g(4) ?
If f(x)= 𝑥 3 -2, and g(x) = 𝑥−2 , what is f(2) / g(2) ?

18. IN GENERAL…what can we say about…
f(x)+g(x)=…
f(x)-g(x)=…
f(x)*g(x)=…
f(x)/g(x)=…
(f+g)(x)
(f-g)(x)
(f*g)(x)
(f/g)(x) As long as g(x) does not equal zero

19. If f(x) = 12x+5, what is f(3)? If f(x) = 12x+5, what is f(y)?
Evaluating functions
If f(x) = 12x+5, what is f(3)?
If f(x) = 12x+5, what is f(y)?
If f(x) = 12x+5, what is f( )?

20. If f(x) = 12x+5, what is f(3 𝑥 2 +7)?
Evaluating functions
If f(x) = 12x+5, what is f(3 𝑥 2 +7)?

21. Composition of functions
The previous example was a composition of functions. Basically, everywhere we had a variable, we replace it with an entirely new function.
This is denoted as 𝑓ᴑ𝑔(x), or as 𝑓(𝑔 𝑥 )

22. Find 𝑓ᴑ𝑔(x) for 𝑓 x =x+3, and g x = 𝑥 2 +7

23. Homework: Section 1.1, pages 9-11: 2, 10, 11, 13-15, 38-40, 42, 44, 47