# 3.6 – Functions and Graphs

Objectives

• Identify ordered pairs in a mapping diagram.
• Identify domain and range using ordered pairs.
• Graphically define the domain and range of a function.
• Use the vertical line test to determine whether a graph is a function.
• Relate a graph to the function it models.

Key Terms

• Ordered Pair – A pair of numbers in parentheses that names the location of a point on a coordinate plane.
• (x,y) is always in alphabetical order.
• Example: (4,-3)
• Graph this point by starting at the origin (0,0), go to the right (x-value) by 4, then go down (y-value) by 3.
• Vertical – Straight up and down.
• On a coordinate plane, the equation of a vertical line is x=a, where a is a constant.
• Horizontal – Straight left and right.
• On a coordinate plane, the equation of a horizontal line is y=a, where a is a constant.
• Vertical Line Test – A method for testing whether a given graph is a function.
• If a vertical line intersects the graph at 2 or more points, it is NOT a function.
• If a vertical line intersects the graph at only 1 point, it IS a function.

Notes

• Example: Is this a function?  Also, find the Domain & Range
• Step 1: Draw a vertical line.  Do you cross the graph once or more than once?
• You cross the graph once, so this IS a function
• Step 2: Domain (all the x-values)
• So, $x \geq 0$
• So, $y \geq 0$