1. Chapter 1 Functions & Graphs Mr. J. Focht PreCalculus OHHS

2. 1.7 Modeling With Functions Functions from Formulas Functions from Graphs Functions from Verbal Descriptions Functions from Data

3. Formulas Into Functions Find a function for the diameter of a circle.

4. Class Work P. 160, #19

5. A Maximum Value Problem Construct an open-topped box from a single sheet of material. The sheet is 10x8 in. Make the box by cutting squares from each corner of the sheet. Fold up each edge. Where should the cuts be made to make a box of largest volume?

6. Make a Drawing 8” 10” x x x x x x x x 10”-2x 8”-2x

7. Describe the Volume as a Function Find the dimensions of the folded box. 10”-2x x 8”-2x Find a function that finds the volume of the box. V(x) = x(10-2x)(8-2x)

8. Find the Maximum Value V(x) = x(10-2x)(8-2x) Find the domain so we can set the viewing window. Since all sides of the box must be positive, 8-2x ≥ 0 or 0 ≤ x ≤ 4

9. Find the Maximum Value To find the range, use the table. Graph. We’ll need to adjust.

10. Find the Maximum Value Find the max.

11. Find the Maximum Value We can see that the cut squares should be 1.47” on each side to give a maximum volume of 52.5 in 3.

12. Class Work P. 161, #33

13. Functions From Graphs A small satellite dish is packaged with a cardboard cylinder for protection. The parabolic dish is 24” in diameter and 6” deep, and the diameter of the cardboard cylinder is 12”. How tall must the cylinder be to fit in the middle of the dish and be flush with the top of the dish? DRAW A PICTURE FIRST

14. Functions From Graphs

15. Function From Graphs y = kx 2 6 = k(12) 2 k= 6 6 Find this y coordinate = 1.5 h h = 6-1.5 = 4.5

16. Class Work P. 161, #35

17. Functions From Verbal Descriptions Grain is leaking through a hole in a storage bin at a constant rate of 8 in 3 per minute. The drain forms a cone-shaped pile on the ground below. As it grows, the height of the cone always remains equal to it radius. If the cone is one foot tall now, how tall will it be in one hour?

18. Functions From Verbal Descriptions Since r = h When h = 1 ft or 12 inches 1 hour later, the volume has grown by Start with the formula Add

19. Functions From Verbal Descriptions The total volume is (576  + 480) in 3. We want to know the height of the cone.

20. Class Work P. 161, #37

21. Using Conversion Factors Find the rps (revolutions per second) of a 15” radius tire on a car traveling 70 miles per hour.

22. Using Conversion Factors Find the circumference of the tire. C = 2  r = 2  (15) = 30  in. 1 revolution = 30  in.

23. Class Work P. 161 #39

24. Functions From Data Later in the course we will learn to “curve- fit” a function to data using our calculator. Do Not Put Numbers in Calc.

25. Functions From Data If we did put the table into our calculator, and plotted them, it would look like this:

26. Functions From Data We try to recognize the shape suggested by the majority of the points.

27. Functions From Data Our calculator can come up with the function for the line (or many other shapes.) We would use this model, also known as a “ regression ” line to predict temperatures.

28. Class Work Look at page 157 to see the regressions our calculator can do, and when we will cover them. Do p. 162, #47 a) b)

29. Home Work P. 160-162, #16, 18, 31, 36, 41-46, 47 c) d)