Advanced Math
Section 2.2 [Day 4]
Name:
Nov. 2015
Vertical/Horizontal Line Test; One-To-One, Increasing/Decreasing/Constant
VERTICAL LINE TEST:
Example 1:
Use the VERTICAL LINE TEST to show whether the given graphs are functions.
a.
b.
c.
d.
HORIZONTAL LINE TEST:
ONE-TO-ONE:
Example 2:
Use the HORIZONTAL LINE TEST to determine which of the functions above are one-to-one
Use the graphs in Example 1 to help answer these questions:
Trace the graph from left to right – your graph is
INCREASING if:
DECREASING if:
CONSTANT if:
 In order to determine the intervals where a graph is increasing, decreasing and/or constant, you first
find the ____ coordinates of the _______________________________________ points.
 For increasing, decreasing and constant intervals, always use the ____________________________
to show the interval notation, unless one of your boundaries is ________ or ________, then use
_____________________________________________.
Example 3:
a.
Label the maximum and minimum values on the graph. Then find the intervals where the
graph is increasing, decreasing and/or constant. Lastly, determine if the function is one-toone.
b.
Increasing:
Increasing:
Decreasing:
Decreasing:
Constant:
Constant:
One-To-One:
One-To-One:
c.
d.
Increasing:
Increasing:
Decreasing:
Decreasing:
Constant:
Constant:
One-To-One:
One-To-One:
Example 3:
e.
Label the maximum and minimum values on the graph. Then find the intervals where the
graph is increasing, decreasing and/or constant. Lastly, determine if the function is one-toone.
f.
Increasing:
Increasing:
Decreasing:
Decreasing:
Constant:
Constant:
One-To-One:
One-To-One:
g.
h.
Increasing:
Increasing:
Decreasing:
Decreasing:
Constant:
Constant:
One-To-One:
One-To-One: