Study Guide: Functions

These web-based activities were developed, during summer sessions from 1997 through 1999, by students at Mainland High School, located in Daytona Beach, FL. As part of Mainland's CCTT grant, the students were given permission by the book's publisher to convert the ancillary materials of the County's adopted Algebra 1 textbook (Glencoe Algebra 1 — ISBN: 9780028253282) into html format.

Study Guide
Functions

As stated in an earlier lesson, functions as a special type of relation.

Example 1: Is {(6, −3), (4, 1), (7, −2), (−3, 1)} a function? Is its inverse a function?

Since each element of the domain is paired with exactly one element of the range, the relation is a function.

However, its inverse is not a function since 1 is paired with more than one element of the range: the values of 4 and −3

inverse: {(−3, 6), (1, 4), (−2, 7), (1, −3)}

The equation y = 2x + 1 can be written as f(x) = 2x + 1.

If x = 3, then f(3) = 2(3) + 1 , or 7.

Thus, f(3), which is read "f of 3," is a way of referring to the value of y that corresponds to x = 3.

Example 2: If f(x) = 3x −4, find f(3) and f(−2)

f(3) = 3(3) − 4

f(3) = 9 - 4

f(3) = 5

f(−2) = 3(−2) − 4

f(−2) = −6 − 4

f(−2) = −10

Directions: Determine whether each relation is a function.

yes, yes, no

yes, no, yes

Given f(x) = 2x - 4 and g(x) = x² −4x, find each value.

4, −4, −14, 21, −⁷/₂ , −¹⁵/₁₆