## Practice Problems

Work through the odd-numbered problems 1-31. Once you have completed the problem set, check your answers.

### Problems

1. If T is the Celsius temperature of the air and v is the speed of the wind in kilometers per hour, then

Determine the Wind Chill Index

(a) for a temperature of 0^{o} C and a wind speed of 49 km/hr and

(b) for a temperature of 11^{o} C and a wind speed of 80 km/hr.

(c) Write a multiline function definition
for the WCI if the temperature is 11^{o} C.

3. Use the graph of in Fig. 19 to evaluate , , , , and . Write a multiline function definition for
.

5. Use the graphs in Fig. 20 and the equation to

determine the values of

(a) Evaluate , and for , and .

(b) Evaluate .

(c) Graph and for .

9.
You are planning to take a one week vacation in Europe, and the tour brochure says that Monday and Tuesday will be spent in England, Wednesday in France, Thursday and Friday in Germany, and Saturday and Sunday in Italy. Let
be the location of the tour group on day d and write a multiline function definition for .

11. Write a multiline function definition for the curve in Fig. 22.

13. Define to be the area of
the rectangle whose lower left corner is at the origin and whose upper right corner is at the point .

a) Evaluate and .

b) Show that for all .

(d) .

17. (a) Let and . Find a value for so that
.

(b) Let and . Find a value for so that .

19. Graph for
. This function is called the "fractional part of " and is an example of a "sawtooth" graph.

21. Modify the function in example 6 to produce a "square wave" graph with a "long on, short
off, long on, short off" pattern.

23. Define to be the slope of the line tangent to the graph of in Fig. 26 at .

(a) Estimate and .

(b) Graph for .

25. Pressing the COS (cosine) button on your calculator several times will produce
iterates of . What number will the iterates approach if you start with and press the COS button 20 or 30 times? What happens if you start with or ? (Be sure your calculator is in radian mode).

C27. Starting with , do the iterates of approach a number? What happens if you
start with or ?

29. Let (a) What are the iterates of f if you start with

Some iterative procedures are geometric rather than numerical.

31. (Optional) Sketch the graph of

Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-1.4-Combinations-of-Functions.pdf

This work is licensed under a Creative Commons Attribution 3.0 License.