LINEAR FUNCTIONS  
Analysis  
1. THE IDENTITY FUNCTION  y = x 
An identity function is a function where its value on the xaxis corresponds to the same number on the yaxis. In other words, the coordinates of each of the points are the same (1,1), (2,2), (3.5,3.5).  
1. Move the red point and look carefully at how all the points on the straight line satisfy the equation y = x. 2. Change the scale to check that it is true for big and small values of x. 

As you can see, the graph of the identity function is a straight line, which bisects the first and third quadrants of the Cartesian coordinates system. All the points on this line have identical coordinates on the xaxis and the yaxis. 
2. THE DOUBLE FUNCTION  
The double function is the function where the value of the yaxis coordinate is worth double the value of the xaxis one, for example:(1,2), (3,6), (4.5,9) etc.  y = 2x 

3. Look carefully at the coordinates of the double function. 4.What do you think the graph of a double function looks like? Draw it in your exercise book. 
3. COMPARING FUNCTIONS  
We are going to compare the graphs of the identity and double functions to see their similarities and differences.  y = x 
y = 2x 

5. Look carefully at the graphs of the identity and double function. 6. In your notebook write down what you think the similarities and differences are between them. 7.What do you think the graphs of the following functions look like: triple, quadruple, quintuple, half, sixth, tenth etc? 
4. LINEAR FUNCTIONS  y = mx  
Now, we are going to look at the graphs of some linear functions:  y = 2x  y = 3x  y = ˝ x  ...  
8. In your exercise book draw four graphs of the following type of functions: triple, quadruple etc, and four graphs of this type of function: half, fifth etc. Find the quickest, easiest way of doing so. 

Juan Madrigal Muga  
Spanish Ministry of Education. Year 2001  
Except where otherwise noted, this work is licensed under a Creative Common License