﻿ RELATIONS - Functions and Graphs - FUNCTIONS - SAT SUBJECT TEST MATH LEVEL 1 ﻿

## CHAPTER 15Functions and Graphs

• Relations

• Functions

• Combining Functions

• Composition of Functions

• Inverse Functions

• Exercises

The concept of a function is one of the most fundamental notions in mathematics. In this chapter, you will see two equivalent definitions of function and then review the most important facts you need to know about functions for the Math 1 test.

### RELATIONS

Since a function is a special type of relation, we will first review the definition of a relation. A relation is a set of ordered pairs. The first and second coordinates of the ordered pairs can be anything whatsoever, although on the Math 1 test they are almost always numbers. The number of ordered pairs in a relation can be finite or infinite. Each of the following sets is a relation:

R1 = {(1, 0), (1, 1), (3, 2)}

R2 = {(0, 1), (1, 1), (2, 1)} = {(xy)| x = 0, 1, or 2 and y = 1}

R3 = {(0, 0), (1, 1), (2, 4)} = {(xy)| y = x2 and x = 0, 1, or 2}

R4 = {(xy)| y = x and x is an integer}

R5 = {(xy)| y = xand x  0}

R6 = {(xy)| y = x 2}

R7 = {(xy)| x = y 2}

R8 = {(xy)| x y = 25}

R9 = {(xy)| x is a state in the United States and y is the capital of x}

R10 = {(xy)| x is a word in the English language and y is the number of letters in x}

R1R2R3R9, and R10 are finite sets with 3, 3, 3, 50, and approximately 400,000 elements, respectively. R4R5R6R7, and R8 are all infinite sets.

Note that (2, 4) is in R3R4R5, and R6; (–1, 1) is in R4 and R6; (, 2) is in R5 and R6; (4, 2) and (4, –2) are in R7.

When the first and second coordinates of the ordered pairs are numbers, you can graph the pairs as explained in Chapter 13 on coordinate geometry. Here are the graphs of R1R2R3R4R5R6R7, and R8.

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