ASSIGNMENT: INTRODUCTION TO FUNCTIONS

1. State whether each is a set. If not, give a brief reason why not.

a. The students in this class

b. The smart students in this class

c. The students over 60 in this class

d. All the sets discussed in this class on Monday

2. State whether each example can represent a function. If so, indicate which is the domain and which is the range. Remember that the each element of the domain must map to exactly one element of the range.

a. On the "rate my prof" website, a number of students have given your instructor a rating on how hard a grader he is.

DOMAIN:

RANGE:

b. On the "rate my prof" website, a particular student has ratedeach of her instructors on how hard a grader he/she is.

DOMAIN:

RANGE:

c. On the "rate my prof" website, consider the set of all students who gave ratings and the set of all professors who were rated on how hard a grader he/she is.

DOMAIN:

RANGE:

3. My google contacts list represents one set. The phone numbers in this directory represents another set. Consider the mapping of people to phone numbers. State whether this is a set and give your reasoning.

4. Does this mapping of set A to set B represent a function? Why or why not?

5. Does this mapping of set A to set B represent a function? Why or why not?

6. Your computer directs each pixel on its screen as to what to display. The computer directs the color by specifying how much blue, red, and yellow to display. (It then has to also direct the saturation and the brightness, but let's leave those out for now.) Consider the set of pixels and the set of colors each takes on in a particular image. Is this a function? Why or why not?

7. This plot represents a function. Remember that a closed circle (a dot) on a point indicates the point is plotted, while an open circle indicates that point is not plotted. So, for example, the point (2,2) is plotted, but the point (3,2) is not. Note that the point (2.9999,2) IS plotted, since the open circle only indicates the endpoint (3,2) is omitted.

a. Describe the range and the domain of this function.

b. Describe in words what this function does. That is, how does it associate the set X with the set Y?