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← Functions and Function Notation

Concept

Function Notation

Function notation is a special way to write functions that explicitly shows that

y

is a function of

x

— in other words, that

y

depends on

x .

Function notation is symbolically expressed as

y = f (x)

and read

y

equals

f

of

x .

Equations that are functions can be written using function notation.

\underline{Equation} y = - 5 x + 4 \underline{Function Notation} f (x) = - 5 x + 4

Notice that

y

has been replaced by

f (x) .

In function notation,

x

represents an element of the domain and

f (x)

represents the element of the range that corresponds to

x .

When written in function notation, the expression that describes how to convert an input into an output — the right-hand side expression — is called the function rule.

f(x)=-5x+4, the right-hand side expression is the function rule

Besides $f,$ other letters such as $g$ or $h$ can be used to name the function. Similarly, letters other than $x$ can name the independent variable.

Extra

Interpreting Function Notation

To interpret an equation given in function notation, it is necessary to understand what both sides of

f (x) = k

mean. For example, consider the following equation.

f (3) = 12

Here,

f (3)

denotes that the function's input is

x = 3

and that

12

is the output corresponding to this input.

f (3) = 12 ⇓ The output of f when x = 3 is 12 .

Now, consider a different scenario. Let

w (t) = 200 t

be a function that describes the number of words Kevin reads in

t

minutes. The following statements are true for this function.

w (4) and w (t) = 900

Here,

w (4)

is the number of words that Kevin reads in

4

minutes and can be found by evaluating the function for

t = 4 .

However, the input is not a particular number in the second statement. In such cases, the statement can be interpreted as a question.

w (t) = 900 ⇓ For which value of t is the output equal to 900 ?

Based on the context, the second statement asks how many minutes it takes Kevin to read

900

words. To find this value of

t,

the equation

w (t) = 900

has to be solved for

t .

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