Chapter 8.2, Problem 2E

Solution

a.

To graph: The function $y=\frac{4}{x-3}-1.5$ after changing the mode on your calculator to CONNECTED.

Given information:

The given function is $y=\frac{4}{x-3}-1.5$ .

Graph:

Now consider the given function:

  $y=\frac{4}{x-3}-1.5$

Press the MODE button in the calculator and highlight the word CONNECTED.

  

Press the $Y=$ button and enter the functions $y=\frac{4}{x-3}-1.5$ .

  

Press GRAPH button in the calculator.

The graph of the function is $y=\frac{4}{x-3}-1.5$

:

  

Interpretation: The graph of the function $y=\frac{4}{x-3}-1.5$ is intersecting the x -axis.

b.

To state: What happens between $x\approx 2.8\text{and}x\approx 3.2$ if you press TRACE and trace the function.

The graph has vertical asymptote between $x\approx 2.8\text{and}x\approx 3.2$ .

Given information:

The given statement says to TRACE and trace the function.

Explanation:

Press TRACE button and trace the function between $x\approx 2.8\text{and}x\approx 3.2$ .

  

There is a sudden jump occurred in the graph between $x\approx 2.8\text{and}x\approx 3.2$ .

It means the graph has vertical asymptote between $x\approx 2.8\text{and}x\approx 3.2$ .

c.

To state: The difference between the in the example and the resultant graph.

The graph disconnects at $x=3$ .

Given information:

The given statement says to what happens to the values of y as x increases and x decreases.

Explanation:

If graph is drawn in CONNECTED mode then the disconnected graph is connected by vertical line $x=3$ .

But if the graph is drawn in a DOT mode then the vertical line $x=3$ will be disappeared.

See the disconnected graph in DOT mode.

  

Therefore, the graph disconnects at $x=3$ .