1. Objective: Students will identify key features of functions.
Mrs. Viney Website
Homework: 3.2 #1-15

2. If we examine a typical graph the function
y = f(x), we can observe that for an interval throughout which the function is defined, that the function might be increasing, decreasing or neither.

16. Extreme Points
A relative extreme point ( relative maximum point or relative minimum point) of a function is a point at which its graph changes from increasing to decreasing or vice versa.

17. A relative maximum point is a point at which the graph changes from increasing to decreasing.

18. A relative minimum point is a point at which the graph changes from decreasing to increasing.

19. The maximum value of a function is the largest value that the function assumes on its domain.
The minimum value of a function is the smallest value that the function assumes on its domain.

20. Note: Functions might or might not have maximum and/or minimum values.

22. Intercepts
We have previously discussed the idea of intercepts. Recall that
The x-intercept is a point at which a graph intersects the x-axis. (x,0)
The y-intercept is a point at which the graph intersects the y-axis. (0,y)

24. Note that a function can have at most one
y-intercept. Otherwise, its graph would violate the vertical line test for a function.
A function may have 0 or more x-intercepts.

25. We now have six categories for describing the graph of a function
Intervals in which the function is increasing or decreasing
Maximum/Minimum values
Domain
Range
x-intercepts, y-intercept
Continuous or Discrete

26. Describe This Function on the interval from (-4,3)

27. 1. Inc (-4, -1.5]
Dec [-1.5, 1.5] Inc [1.5, 3)
Max (-1.5, 14) Relative Maximum is 14 Min (1.5, -1) Relative Minimum is -1
Domain (-4, 3)
Range (-4, 16)
y-intercept = 6 (0,6) x-intercepts = -3, 1, 2 (-3,0) (1,0) (2,0)
Continuous