Functions Unit Pre-Algebra

VOCABULARY! EXAMPLES! Relation: Domain: Range: Function: Functions can be represented by: Graphs Tables Ordered Pairs Function Rules A set of ordered pairs The set of all the input (x) values The set of all the output (y) values A special relation that has exactly ONE output for each input (or exactly ONE y value for each x value) ( , ) y = 2x + 1 y = 4x y = x2 -1 Input Output

Input-Output Tables By looking at each input-output table, tell whether or not the relation is a function. If it is a function, state the domain and range. 1. 3. 2. 4. Input Output x y Input Output x y

Make an input-output table for a function given a specific domain. State the range of the function. 5. 7. 6. 8.

To create an input-output table from the given rule: Step 1: 1. 3. Step 2: 2. 4. Choose values for x (It is best to choose two negative values, zero, and two positive values). Evaluate the function at these values and complete the input-output table.

To create a function rule from the following input-output tables: 1. 3. 5. 4. 2. 6. “What can I do to the input to get that output?” THINK! OR “What can I do to the x to get that y?”

VERTICAL LINE TEST GRAPHS can represent functions. The ____________________ ___________ __________ can help you test whether or not a graph is a function. Remember: There can only be ONE y value for each x value. If you run your pencil across two points vertically above one another, it is NOT a function! Determine which graphs are functions VERTICAL LINE TEST

To graph each function by creating a table of values of first: Step 1: Choose values for x Step 2: Evaluate the function at Step 3: Plot the points on a (it is best to choose two these values and complete coordinate plane and negative values, zero, the input-output table. graph the function. and two positive values). 1. x y = 2x 3. x y = - x -2 -1 1 2 2. x y = x - 3 4. x

Make an Input-Output Table from the given graph: Step 1: Find where the graph Step 2: Create an Input-Output Step 3: Find the pattern in the crosses at lattice points. Table from those ordered pairs. table to create a function rule. Draw those dots in larger. 1. x y 3. -2 -1 1 2 2. 4.