1. Dr. Fowler  CCM
Functions

2. Vocabulary Iteration – A repetitive process
Recursive Equation – shows how to calculate the next term from the current
Sequence – List where each item is based on previous terms using a pattern
Domain – the set of all X values
Range – the set of all Y values
Independent Variable – a variable like X whose values DO NOT depend on another
Dependent Variable – a variable like Y whose values DO depend on another

3. How would you use your calculator to solve 52?
Input
Output
Press: 5 x2 25
The number you entered is the input number (or x-value on a graph).
The result is the output number (or y-value on a graph).
The x2 key illustrates the idea of a function.

4. Graph Equation Table of values A set of ordered pairs Mapping
A function is a relation that gives a single
output number for every valid input number.
A relation is a rule that produces one or more
output numbers for every valid input number.
There are many ways to represent relations:
Graph
Equation
Table of values
A set of ordered pairs
Mapping
These are all ways of showing a relationship between two variables.

5. A function is a rule that gives a single output number
for every valid input number.
To help remember & understand the definition:
Think of your input number, usually your x-coordinate, as a letter.
Think of your output number, usually your y-coordinate, as a mailbox.

6. A function is a rule that gives a single output number
for every valid input number.
Input number
Output number
Can you have one letter going to two different mail boxes?
Not a FUNCTION

7. A function is a rule that gives a single output number
for every valid input number.
Input number
Output number
Can you have two different letters going to one mail box?

8. Are these relations or functions?
&
Relation x y 1 2 3 4
x y 5 6 7 5 6 7

9. Are these relations or functions?
Not a Function but a
Relation x y
x y 5 6
1 7
1 6 1 2 5 6 7

10. Are these relations or functions?x y
Not a function
But a relation 5 6 8 11 1 2 3
x y 5 6 11 8

11. These all represent the SAME function!
In words:
Double the number and add 3
As an equation:
y = 2x + 3
These all represent the SAME function!
As a table of values:
x y
-1 1
0 3
1 5
As a set of ordered pairs:
(-2, -1) (-1,1) (0,3) (1, 5) (2, 7) (3, 9)

12. Functional Notation
An equation that is a function may be expressed using functional notation.
The notation f(x) (read “f of (x)”) represents the variable y.

13. Functional Notation Cont’d
Example:
y = 2x + 6 can be written as f(x) = 2x + 6.
Given the equation y = 2x + 6, evaluate when x = 3.
y = 2(3) + 6
y = 12

14. Functional Notation Con’t
For the function f(x) = 2x + 6, the notation f(3) means
that the variable x is replaced with the value of 3.
f(x) = 2x + 6
f(3) = 2(3) + 6
f(3) = 12

15. Evaluating Functions Given f(x) = 4x + 8, find each: f(2) 2. f(a +1)
= 4(2) + 8
= 16
= 4(a + 1) + 8
= 4a
= 4a + 12
= 4(-4a) + 8
= -16a+ 8

16. Evaluating More Functions
If f(x) = 3x  1, and g(x) = 5x + 3, find each:
f(2) + g(3)
= [3(2) -1] + [5(3) + 3] =
= 23
f(4) - g(-2)
= [3(4) - 1] - [5(-2) + 3]
= (-7)
= 18
f(1) + 2g(2)
= 3[3(1) - 1] + 2[5(2) + 3] =
= 32

17. Excellent Job !!! Well Done