functions

functions

Lesson Preview

What You'll Learn

variable: a symbol, or letter, representing a quantity capable of assuming any of a set of values

function: a secondary variable related to some original variable by a rule of correspondence such that, for any value assigned to the first, there is one and only one value determined for the second

What are functions and how do you use the notation with which functions are associated?

How do you draw the graph of a function?

How do you use δΔx to mean an increase in ---?

Vocabulary You Need to Know

l l l l l l l l l l l l l l l l l l l l l

You might think of a function as a unique value assigned to a second variable as a result of a rule being applied to the value of some original variable. In this case the rule was, “Get y by multiplying x times itself.” Consequently, y is a function of x.

Attention: Note that the term “function” applies both to the second value and to the rule that generated that value. In the above example, y is a function of x, and at the same time, the rule: is also a function.

(Remember also that f (x) = y is read, “The function of x equals y.”)

f (x) = y

y = x

You may recall from algebra that a variable is a letter that stands for an unknown number. You may also recall that a function is a variable related to another variable in such a way that, for each value assumed by the first, there is one and only one value determined for the second.

In this illustration, y is a funtion of x because the value of y depends on x. You start with a value for x, and then you apply some rule to determine the value for y. The value of x determnines the value of y -- so y is a “function” of x.

2a What Are Functions?

y = x