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-intercept, 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 left to right Decreasing : the graph goes down from left to right Extrema : points of relatively high or low function value -Relative Minimum : no other points have a lesser y- coordinate -Relative Maximum : no other points have a greater y- coordinate 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 (you could also say it will never be negative since you will never have a negative population of deer, the smallest it could be is 0) Increasing:between about 1 < x < 4 Decreasing: 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.

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 (you could also say it is never negative for this particular graph) Increasing: x <1 and between 4 < x < 6 Decreasing: 1 6 Relative Extrema: -Relative x= 1 and x=6 -Relative x = 4 End Behavior: As x increases, y decreases. As x decreases y decreases. Example 3: