Functions (Notation and Evaluating)

Definitions

Relation A relationship between sets of information. Typically between inputs and outputs.

Function A relation such that there is no more than one output for each input

4 Examples of Functions

X Y

-3 1

-1 0

0 4

5 7

7 3

X Y

10 2

15 -5

18 -5

20 1

7 -5

3 Examples of Non-Functions

X Y

0 4

1 10

2 11

1 -3

5 3

Function NotationThe f is the name of the function machine and

the value inside the parentheses is the input. The expression to the right of the equal sign shows what the machine does to the input.

25f

Which do you prefer to write?

OREvaluate f when

x = 25?

25

5

Example

If f(x) = 2x + 3, find f(5).

5f 2 5 3

5 10 3f

5 13f

You want x=5 since f(x) was

changed to f(5)

When evaluating, do not write f(x)!

You wanted to find f(5). So the complete final

answer includes f(5) not f(x)

Solving v. Evaluating

23If 3, complete the following:f x x

a. Evaluate 3f b. Find if 5x f x Substitute and Evaluate

The input (or x) is 3.

Solve for x

The output is -5.

23 3 3 2

35 3x

No equal sign Equal sign

2 3

1

238 x

12 x