<< Chapter < Page Chapter >> Page >

We can also give an algebraic expression as the input to a function. For example f ( a + b ) means “first add a and b , and the result is the input for the function f .” The operations must be performed in this order to obtain the correct result.

Function notation

The notation y = f ( x ) defines a function named f . This is read as y is a function of x . The letter x represents the input value, or independent variable. The letter y ,  or f ( x ) , represents the output value, or dependent variable.

Using function notation for days in a month

Use function notation to represent a function whose input is the name of a month and output is the number of days in that month.

The number of days in a month is a function of the name of the month, so if we name the function f , we write days = f ( month ) or d = f ( m ) . The name of the month is the input to a “rule” that associates a specific number (the output) with each input.

The function 31 = f(January) where 31 is the output, f is the rule, and January is the input.

For example, f ( March ) = 31 , because March has 31 days. The notation d = f ( m ) reminds us that the number of days, d (the output), is dependent on the name of the month, m (the input).

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Interpreting function notation

A function N = f ( y ) gives the number of police officers, N , in a town in year y . What does f ( 2005 ) = 300 represent?

When we read f ( 2005 ) = 300 , we see that the input year is 2005. The value for the output, the number of police officers ( N ) , is 300. Remember, N = f ( y ) . The statement f ( 2005 ) = 300 tells us that in the year 2005 there were 300 police officers in the town.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Use function notation to express the weight of a pig in pounds as a function of its age in days d .

w = f ( d )

Got questions? Get instant answers now!

Instead of a notation such as y = f ( x ), could we use the same symbol for the output as for the function, such as y = y ( x ), meaning “ y is a function of x ?”

Yes, this is often done, especially in applied subjects that use higher math, such as physics and engineering. However, in exploring math itself we like to maintain a distinction between a function such as f , which is a rule or procedure, and the output y we get by applying f to a particular input x . This is why we usually use notation such as y = f ( x ) , P = W ( d ) , and so on.

Representing functions using tables

A common method of representing functions is in the form of a table. The table rows or columns display the corresponding input and output values. In some cases, these values represent all we know about the relationship; other times, the table provides a few select examples from a more complete relationship.

[link] lists the input number of each month (January = 1, February = 2, and so on) and the output value of the number of days in that month. This information represents all we know about the months and days for a given year (that is not a leap year). Note that, in this table, we define a days-in-a-month function f where D = f ( m ) identifies months by an integer rather than by name.

Month number, m (input) 1 2 3 4 5 6 7 8 9 10 11 12
Days in month, D (output) 31 28 31 30 31 30 31 31 30 31 30 31

[link] defines a function Q = g ( n ) . Remember, this notation tells us that g is the name of the function that takes the input n and gives the output Q  .

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Precalculus' conversation and receive update notifications?

Ask