Library of Functions

							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

Shawna has kindly given permission for this resource to be downloaded
from www.mathxtc.com and for it to be modified to suit the Western
Australian Mathematics Curriculum.



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