1. Functions Unit
Pre-Algebra

2. 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

3. 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.
Input
Output x y
Input
Output x y

4. Make an input-output table for a function given a specific domain.
State the range of the function.

5. To create an input-output table from the given rule:
Step 1:
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.

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

7. 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

8. 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).
x y = 2x x y = - x -2 -1 1 2
x y = x x

9. 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.
x y 3. -2 -1 1 2