1. SFM Productions Presents: Another exciting episode of your continuing Pre-Calculus experience! 1.5 Analyzing Graphs of Functions

2. Homework for section 1.5 P 619-13, 21-31, 39-41, 45, 57, 59, 63, 65, 69, 71, 77, 79, 83-89, 101-109, 113

3. y = f(x) x X = distance from y-axis f(x) = distance from x-axis f(x) (x,y) = (x,f(x))

4. Domain: x-values (legal) Range: y-values (obtained from inserting the domain values into function) D: [-3,6) R: [-7.5,5] domain range f(-3) = f(-1) = -4 5 f(4) = -7.3ish f(x) = y

5. Example:

6. Therefore, this is not a function. Vertical Line test:A relation is a function if a vertical line intersects the graph in only 1 point.

7. Therefore, this is a function. Vertical Line test:A relation is a function if a vertical line intersects the graph in only 1 point.

8. Therefore, this is a function. Vertical Line test:A relation is a function if a vertical line intersects the graph in only 1 point.

9. Describe what a graph looks like - what is it doing? Always done from left to right - is the graph going higher or lower? Decreasing Constant Increasing left to right: means you are only interested in the x-values.

10. Increasing: Decreasing:

11. Local Maxima (Relative Maxima) Local Minima (Relative Minima) Just another way to describe what is happening in a graph.

12. How to approximate relative maximums and minimums using the calculator…

13. Even and Odd functions A graph is symmetric with respect to the y-axis if whenever the point (x, y) is on the graph, so is the point (- x, y). Such graphs are called EVEN. You can show a function to be even either graphically or algebraically.

14. Even and Odd functions A graph is symmetric with respect to the origin if whenever the point (x, y) is on the graph, so is the point (- x, -y). Such graphs are called ODD. You can show a function to be odd either graphically or algebraically.

15. Even and Odd functions A graph is symmetric with respect to the x-axis if whenever the point (x, y) is on the graph, so is the point (x, -y).

16. Average Rate of Change One of the definitions of slope of a line is rate of change. For a curve whose slope changes at each point, we can calculate the average rate of change. The calculation is similar to slope. Lets find the average rate of change from x 1 =-2 to x 2 =0.

18. Go! Do!