SWBAT: interpret positive, negative, increasing, and
decreasing behavior, extrema, and end behavior of graphs
of functions.
• Why?
Sales of video games, including hardware, software, and
accessories, have increased at times and decreased at
other times over the years. Annual retail video game sales
in the U.S. from 2000 to 2009 can be modeled by the graph
of a nonlinear function.
• Why would a linear function not model the sale
of video games well?
• Describe some points or area on a graph of
video game sales that might be of more interest
to someone in the video game industry than
other points.
x-intercept : the x-coordinate of the point at which a graph
intersects the x-axis. At the x-axis y=0
y-intercept : the y-coordinate of the point at which the graph
intersects the y-axis. At the y-intercept x =0.
Graph and Function Behavior
Positive : the graph is above the x-axis
Negative : the graph is below the x-axis
Increasing : the graph goes up from right to left
Decreasing : the graph goes down from right to left
Extrema : points of relatively high or low function value
-Relative Minimum : no other points have a lesser ycoordinate
-Relative Maximum : no other points have a greater ycoordinate
End Behavior – describes the values of a function at the
positive and negative extremes in its domain
Example 1:
Example 2:
Positive:
0 < x < 5.7
Negative:
for about x > 5.7
Increasing: between about 1 < x < 4
Decreasing: x < 1 and x > 4
Relative Maximum:
at about x = 4
Relative Minimum:
at about x = 1
End Behavior: As x increases, y decreases. As x
decreases y increases.
Example 3:
SPEED The graph shows the speed of a car after x minutes. Estimate
and interpret where the function is positive, negative, increasing,
and decreasing, and the x-coordinates of any relative extrema, and
the end behavior of the graph.
Positive: 0< x < 7.2
Negative: x >7.2
Increasing: x <1 and between 4 < x < 6
Decreasing: 1 < x < 4 and x> 6
Relative Extrema:
-Relative Maximum @ x= 1 and x=6
-Relative Minimum @ x = 4
End Behavior: As x increases, y decreases. As x
decreases y decreases.