1. Functions Learning Objectives To understand function notation
To be able to substitute and perform calculations with functions
To know the difference between a function and a relation
Notation:
f(x) = 3x + 1 says function f maps x to 3x + 1
g:x √x says function g maps x to the square root of x cubed -5.
Functions are often given the letter f, but any other can also be used.

2. Substitution with functions
f(x) = x2 - 5
Find f(x) when i) x = 5, ii) x = -3 iii) x = 0
f(5) = =
= 20
f(-3) = (-3)2 - 5
= 9 - 5
= 4
f(0) =
= - 5
f:x -> 1/(x - 5)
Find f:x when i) x = 6, ii) x = 3 iii) x = 0
f:x -> 1/(6 - 5)
-> 1/1
-> 1
f:x -> 1/(3 - 5)
-> 1/(-2)
-> -1/2
f:x -> 1/(0-5)
-> -1/5
what happens when x = 5?

3. Not a function Many to Many This is a function! One to one This is a
So the difference between a function and a relation is...
Think about mappings:
This is a function!
One to one
This is a
Function!
Many to one
Not a function
One to Many
Not a
function
Many to Many

4. Domain and Range
"the input values"
"the allowed output values"

6. Substituting Algebra in Functions
f(x) = 3x + 2 find i) f(5) ii) f(-5) iii) f(-x) vi) f(x+5)

7. More complicated...
f(x) = x2 - 3x find i) f(2x) ii) 2f(x) iii) 1 - f(x+1)