Basic Function Objectives

The student who understands the function concept:
 
1.  For a given  function, has the ability to identify the output for a given input.

1a.  For a given  function, has the ability to identify the outputs for a given set of inputs (for example all x-values greater than 3, or all x-values between 1 and 5).
 
2.  For a given  function, has the ability to identify input(s) for a given output.

2a.  For a given  function, has the ability to identify the inputs for a given set of outputs (for example all y-values greater than 3, or all y-values between 1 and 5).
 
3.  For a given  function, has the ability to identify (input, output) pairs (ordered pairs).
 
4.  For a given function, has the ability to identify the domain of the function.  (This includes identification of values that are not in the domain.)
 
5.  For a given function, has the ability to identify the range of the function.  
 
6.  Given representations of two functions, has the ability to determine if the two representations are the same function.
 
7.  Has the ability to transfer from one representation (algebraic, numeric, graphic, or verbal) of a function to another (especially for certain families of functions).  In other words, given one of the four representations, produce the other three representations.
 
8.  Has the ability to determine the values of the domain for which the function values are increasing. 

9.  Has the ability to determine the values of the domain for which the function values are  decreasing.