1. Unit 2 Lesson 1
Function Definitions

2. Function vs. Relation Function:
Is a special relation in which each input gives only one output.
Relation:
Is a comparison of two numbers.
Examples:
{(1, 2), (2, 3), (3, 4)} notice each input has only one output!
{(1, 2), (2, 2), (3, 2)} again notice how each input has only one output.
Examples:
{(1, 3), (1, 4), (2, 5)} notice how the input 1 has two different outputs, this is not a function, but it is a relation.
{(1, 2), (1, 3), (1, 4)} again notice how the same input has different outputs.

3. Parts of a function Domain:
The domain of a function is the list of all possible input values.
Range:
The range of a function is the list of all possible output values.
Example:
{(1,2), (2, 3), (3, 4)} is a function.
The domain of the function is the list of the inputs : {1, 2, 3}
The range of the function is the list of the outputs: {2, 3, 4}

4. Function notation
We often use f(x) (say “f of x”) to represent functions.
For example:
f(x) = 2x is a definition of a function. In this definition, each input is multiplied by 2 in order to arrive at an output.
Using function notation allows us to use function rules to find input and output values.

5. Function notation continued…
Example:
Let f(x) = 3x + 1. Find f(4).
*f(4) means to evaluate the function for the input value of 4*
Substituting 4 for x we now have:
f(4) = 3(4) + 1
f(4) = = 13
f(4) = 13
We can also write the solution as the ordered pair (4, 13).

6. Your turn
Evaluate the following function rules for the given input values 1. f(x) = 3x – 4, find f(2). 2. g(x) = -2x + 7, find g(7).

7. Solutions
1. f(2) = 2
2. g(7) = -7

8. Next steps…. Be sure to watch the videos for this lesson!
Also, take the quiz with this lesson.