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

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.

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.

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

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

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.

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

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)

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.

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

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

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