Chapter 8.3, Problem 24PPS

a.

To determine

To write an equation representing the density of the unknown as a function of volume.

Answer to Problem 24PPS

The required function is $d=\frac{200}{v}$ .

Explanation of Solution

Given information:

The given statement is:

“Parker has $200\text{ grams}$ of an unknown liquid. Knowing the density will help him discover what type of liquid that is.”

The density of the liquid is $d$ and the volume is $v$ .

The equation representing the density as a function of volume can be written as:

  $d=\frac{200}{v}$ .

Hence, the required function is $d=\frac{200}{v}$ .

b.

To determine

To graph the function.

Explanation of Solution

Given information:

The given function is:

  $d=\frac{200}{v}$

Graph:

The graph of the function is:

  

c.

To determine

To identify the asymptotes, domain and range of the function.

Answer to Problem 24PPS

The asymptote is at $v=0\text{ and }d=0$ .

The domain of the graph is all real numbers not equal to $0$ and the range is all real numbers except $0$ .

Explanation of Solution

Given information:

The given statement is:

“Parker has $200\text{ grams}$ of an unknown liquid. Knowing the density will help him discover what type of liquid that is.”

The function is $d=\frac{200}{v}$ .

This represents a transformation of the graph of $f\left(x\right)=\frac{1}{x}$ .

  $a=150$ : The graph is expanded.

  $h=0$ : There is an asymptote at $v=0$ .

  $k=0$ : There is an asymptote at $d=0$ .

The asymptote is at $v=0\text{ and }d=0$ .

The domain of the graph is all real numbers not equal to $0$ and the range is all real numbers except $0$ .