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 10 2 15 -5 18 20 1 7 X Y -3 1 -1 4 5 7 3

3 Examples of Non-Functions Y 4 1 10 2 11 -3 5 3

Which do you prefer to write? Function Notation The 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. 25 Which do you prefer to write? Evaluate f when x = 25? OR 5

Example If f(x) = 2x + 3, find f(5). When evaluating, do not write f(x)! You want x=5 since f(x) was changed to f(5) You wanted to find f(5). So the complete final answer includes f(5) not f(x)

Substitute and Evaluate Solving v. Evaluating No equal sign Equal sign Substitute and Evaluate The input (or x) is 3. Solve for x The output is -5.