# Library of Functions

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```							You should be familiar with the shapes of
Library of Functions
these basic functions.
Equations that can be
written f(x) = mx + b

slope      y-intercept

The domain of these functions
is all real numbers.
f(x) = 3        f(x) = -1            f(x) = 1

Constant Functions
f(x) = b, where b is a real number
Would constant
The domain of these functions     functions be even
is all real numbers.              or odd or neither?

The range will only be b
If you put any real
number in this function,
you get the same real
number “back”.
f(x) = x

Identity Function
f(x) = x, slope 1, y-intercept = 0
Would the identity
function be even
The domain of this function is          or odd or neither?
all real numbers.

The range is also all real numbers
Square Function
f(x) = x2
Would the square
function be even
The domain of this function is   or odd or neither?
all real numbers.

The range is all NON-NEGATIVE real numbers
Cubic Function
f(x) = x3
Would the cube
function be even
The domain of this function is   or odd or neither?
all real numbers.

The range is all real numbers
Square Root Function
f x   x      Would the square
root function be
The domain of this function is   even or odd or
NON-NEGATIVE real numbers.       neither?

The range is NON-NEGATIVE real numbers
f x  
1
x

Reciprocal Function
The domain of this function is   Would the
all NON-ZERO real numbers.       reciprocal function
be even or odd or
neither?

The range is all NON-ZERO real numbers.
f x   x

Absolute Value Function
The domain of this function is     Would the
all real numbers.                  absolute value
function be even
or odd or neither?

The range is all NON-NEGATIVE real numbers
Acknowledgement

I wish to thank Shawna Haider from Salt Lake Community College, Utah
USA for her hard work in creating this PowerPoint.

www.slcc.edu

from www.mathxtc.com and for it to be modified to suit the Western
Australian Mathematics Curriculum.

Stephen Corcoran
St Stephen’s School – Carramar
www.ststephens.wa.edu.au

```
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