y = x

An identity function is a function where its value on the x-axis corresponds to the same number on the y-axis. 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 x-axis and the y-axis.

The double function is the function where the value of the y-axis coordinate is worth double the value of the x-axis one, for example:(1,2), (3,6), (4.5,9) etc.

y = 2x

You can move the red point with the mouse or the little arrows and also change the value of x.

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.

We are going to compare the graphs of the identity and double functions to see their similarities and differences.

y = x

y = 2x

You can move the red point with the mouse or the little arrows and you can also change the value of x.

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?

Now, we are going to look at the graphs of some linear functions: y = 2x y = 3x y = ˝ x ...
You can see the graphs of some linear functions by using the m control button.

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

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