Exercise 7 Page 156

We will determine whether the following function is continuous or discontinuous using a graphing calculator. Note that a function is continuous if its graph has no breaks, holes, or gaps. f(x)=x Let's draw the graph of the function! To draw a graph on a calculator, we first press the Y= button and type the function in one of the rows. Having written the function, we can push GRAPH to draw it.

When we draw a graph on a graphing calculator, the default viewing window is the standard viewing window, which has the following settings.

However, to see if the graph has a hole, the dimensions of the window must be proportional with the dimensions of the calculator screen in terms of the number of pixels. For our screen, which is 63 pixels high and 95 pixels wide, we use a viewing window setting as follows.

Looking at the graph, we can see that it has no breaks, holes, or gaps. Therefore, the function is continuous.

Extra

Determining a Viewing Window

To think about how to determine a viewing window size, let's consider the following viewing window — it is 63 pixels high and 95 pixels wide.

In this screen, there are 47 pixels on both sides of the y-axis. Note that the y-axis is also counted as 1 pixel. Therefore, in total, there are 95 pixels horizontally. By the same logic, there are 63 pixels vertically.

With the viewing window settings, we can conclude that each pixel maps to a single integer value on each axis. Thus, to see the pixels at the corresponding x-values, the dimensions of the window must be proportional with the dimensions of the screen in terms of the number of pixels.