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# Relations and Functions Help (page 3)

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By — McGraw-Hill Professional
Updated on Aug 26, 2011

## Domain and Range

Let f be a function from set A to set B. Let A' be the set of all elements a in A for which there is a corresponding element b in B. Then A' is called the domain of f.

Let f be a function from set A to set B. Let B' be the set of all elements b in B for which there is a corresponding element ain A. Then B' is called the range of f.

## Relations and Functions Practice Problems

#### Practice 1

Figure 1-2 is called a Venn diagram. It shows two sets A and B, and three points or elements P, Q, and R. What is represented by the cross-hatched region? Which of the points, if any, is in the intersection of sets A and B? Which points, if any, are in the union of sets A and B?

#### Solution 1

The cross-hatched region represents all the elements that are in both set A and set B, so it is an illustration of A B, the intersection of A and B. None of the elements shown are in A B. Points P and Q are in A B, the union of A and B.

#### Problem 2

Figure 1-3 is an illustration of a relation that maps certain points in a set C to certain points in a set D. Only those points shown are involved in this relation. Is this relation a function? If so, how can you tell? If not, why not?

#### Solution 2

The relation is a function, because each value of the independent variable, shown by the points in set C, maps into at most one value of the dependent variable, represented by the points in set D.

Practice problems for these concepts can be found at:

Background Math Practice Test

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