Chapter 8.2, Problem 1E

Solution

a.

To graph: The parent reciprocal function $y=\frac{1}{x}$ .

Given information:

The given function is $y=\frac{1}{x}$ .

Graph:

Now consider the given function:

  $y=\frac{1}{x}$

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

  

Press the $Y=$ button and enter the functions $y=\frac{1}{x}$ .

  

Press GRAPH button in the calculator.

The graph of the function is $y=\frac{1}{x}$

:

  

Interpretation: The graph of the function $y=\frac{1}{x}$ will never touch the x -axis and the y -axis.

b.

To state: Both the negative and positive values of x . Also describe what happens to the y -values as x approaches zero.

If x approaches to zero from right, then the y values are approaching to $+\infty$ and if as x approaches to zero from the left, y values are approaching to $-\infty$ .

Given information:

The given statement says to state the negative and positive values of x and describe what happens to the y -values as x approaches zero.

Explanation:

Consider the graph from part (a),

  

It can be seen from the graph that as x approaches to zero from right, then the y values are approaching to $+\infty$ .

Similarly, as x approaches to zero from the left, y values are approaching to $-\infty$ .

c.

To state: What happens to the values of y as x increases and x decreases.

If x increases, the values of y approaches to 0 and x decreases values of y approaches to 0.

Given information:

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

Explanation:

Consider the graph from part (a),

  

It can be seen from the graph that as x increases the y values are approaching to 0.

Similarly, as x decreases, y values are approaching to 0.

Therefore, as $x\to \pm \infty$ the values of y tends to zero.