Exercise 1 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. Let's draw the graph of the function! To draw a graph on a calculator, we first press the $\boxed{\text{Y}=}$ button and type the function in one of the rows. Having written the function, we can push $\boxed{\text{GRAPH}}$ 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.

Even if it is hard to see there is a hole at $(0,\text{-}1),$ so the function is discontinuous. We can also verify this by using the table feature of the calculator. To do so, we push $\boxed{2\text{ND}}$ and $\boxed{\text{WINDOW}}.$ Then, we change the settings as follows.

Having changed the settings, we push $\boxed{2\text{ND}}$ and $\boxed{\text{GRAPH}}$ to get a table of values of the function.

Since the function is undefined at $x=0,$ we can verify that it is discontinuous.