Section 1.3 Worksheet:

Assigned problems: Exercises pp. 46-49, #1, 3, 5, 6, 20, 27, 30, 54 (due Wednesday)

1. What kind of transformation of a function given by the formula f(x) results in a vertical scaling of the function's graph? a vertical shift?

2. What is the difference between a sum of two functions, f + g and a composition of two functions, ?

3. For a composition of two functions to exist, , what must be true about the domains and ranges of the functions?

4. In a composition of two functions, , which function acts first?

5. Some functions can be written as compositions in more than one way. Can you give an example?

6. Is the model in Example 4 (p. 41) a theoretical model, or an empirical model? Explain.

Notes:

1. Compositions are of fundamental importance. You need to be familiar and comfortable with them! Note especially the impact of the absolute value function (e.g. Example 5, p. 27).
2. Remember that angles will be measured in radians almost always in this class! You should know how to convert between radians and degrees, however.