Knowing the rule that defines a function can be very useful. It can help us to:

• Find the output when we know the input.

  • If the rule defines , we can find by evaluating .
  • If defines function , we can find by evaluating .

• Create a table of values.

  Here are tables representing functions and :

  0	10
  1	15
  2	20
  3	25
  4	30

  0	3
  1
  2	2
  3
  4	1

• Graph the function. The horizontal values represent the input, and the vertical values represent the output.

  For function , the values of are the vertical values, which are often labeled , so we can write . Because is defined by the expression , we can graph .

  For function , we can write and graph .

  

  Graph of a line, origin O. X axis from negative 4 to 4, by 2s. Y axis from negative 20 to 20, by 20s. Line passes through points negative 4 comma negative 10, negative 2 comma 0, 0 comma 10, and 2 comma 20.

  

• Find the input when we know the output.

  Suppose the output of function is 65 at some value of , or , and we want to find out what that value is. Because is equal to , we can write and solve for .

Each function here is a linear function because the value of the function changes by a constant rate and its graph is a line.