"

Unit 4.6 Introduction to Functions

Functions

Functions are relations between sets of inputs (x) and outputs (y). Often these inputs and outputs are called domain and ranges.

Where x values are domain values and y values are range values. These are the values where the equation is defined. An equation is only a function if each input has exactly one output.

y = x  is a function because if you plug in an x value, you get exactly 1 y value.

y = ± x is not a function because x could be positive or negative. giving two different y values.

Functions

Example 1:

For the ordered pairs (1,2) (5,4) (7,8) and (3, 4), does this represent a function?

List and group all x and y values

Because each x value is unique, and only has one y value (one arrow), these ordered pairs represent a function

Example 2:

For the ordered pairs (1,5) (1,4) (4,4) (6, 7) does this represent a function?

Because one of our x values has two arrows, i.e. it has two y values, it is not a function

 

One way to tell if an equation is a function is to do a “vertical line test”. You draw a vertical line through your graph. If it crosses the shape more than once, it is NOT a function

Function                                                                        Not a Function

   

Function Notation

Functions are often notated using function notation.

f(x) = x

this is no different than saying

y = x

We replace the “y” with the value “f(x)”. In this case we are saying that “f” is a function of “x”. It can be any letter combination so long as the “x” is a defined variable within the function

For example:

h(a) = a + 1

h is a function of a, where a is the variable

 

 

 

License

ESET1140: Intermediate Technical Algebra Copyright © 2024 by froenico. All Rights Reserved.