1.3 Graphs of Functions

1. 1.3 Graphs of Functions Students will find the domain and range of functions and use the vertical line test for functions. Students will determine intervals on which functions are increasing, decreasing, or constant. Students will determine relative maximum and relative minimum values of functions. Students will identify and graph step functions and other piecewise-defined functions. Students will identify even and odd functions.

2. Example 1: Use the graph • Find the domain of f(x) • Find f(-1) • f(2) • Find the range of f(x) *When viewing a graph of a function, realize that solid or open dots on the end of a graph mean that the graph doesn’t extend beyond those points. However, if the circles aren’t shown on the graph it may be assumed to extend to infinity.

3. Example 2 Find the domain and range of

4. Example 3 Use the vertical line test to decide whether the graphs in Figure 1.21 on p.31 represent y as a function of x.

5. Increasing, Decreasing, and Constant Functions A function is increasing if it is moving upward (or uphill) as a graph moves from left to right. This would be similar to a line with a positive slope. A function is decreasing if it is moving downward (or downhill) as a graph moves from left to right. This would be similar to a line with a negative slope. A function is constant if it is not increasing or decreasing such as in a horizontal line. This would be similar to a line with a slope of zero.

6. Example 4 In figure 1.23 on p. 32, determine the open intervals on which each function is increasing, decreasing, or constant.

7. Relative minimum and relative maximum points A point is a relative minimum if each point nearest on the right and nearest on the left are above the point. A point is a relative maximum if each point nearest on the right and nearest on the left are below the point.

8. Example 5: Relative Minimum/Relative Maximum Use a graphing calculator to approximate the relative minimum of the function given by

9. Example 6 Use a graphing calculator to approximate the relative minimum and relative maximum of the function given by

10. Example 7 During a 24-hour period, the temperature y (in degrees Fahrenheit) of a certain city can be approximated by the model where x represents the time of day, with x = 0 corresponding to 6 a.m. Approximate the maximum and the minimum temperatures during this 24-hour period.

11. Example 8 Sketch the graph of f(x)={

12. Example 9 Is the function given by even, odd.or neither?

13. Example 10 a. b. c.