Chapter ISG, Problem 7.3.7P

a.

To determine

To graph the given function

Explanation of Solution

Given information:

The function is,

  $y=x^{\frac{1}{3}}$

Graph:

  

b.

To determine

To graph the given function

Explanation of Solution

Given information:

The given function is,

  $y=x^{\frac{5}{3}}$

Graph:

  

c.

To determine

To graph the given function

Explanation of Solution

Given information:

The function is,

  $y=x^{\frac{2}{3}}$

Graph:

  

d.

To determine

To graph the given function

Explanation of Solution

Given information:

The given function is,

  $y=x^{\frac{9}{3}}$

Graph:

  

e.

To determine

To evaluate the pattern

Answer to Problem 7.3.7P

The pattern these graphs make is called cubic graph

Explanation of Solution

Given information:

Graph of $y=x^{\frac{1}{3}}$ , graph of $y=x^{\frac{5}{3}}$ , graph of $y=x^{\frac{2}{3}}$ and graph of $y=x^{\frac{9}{3}}$

  

  

Concept Used: Graphical analysis

The pattern these graphs make is called cubic graph. Cubic graph is a 3-regular graph. It is called trivalent graphs.

f.

To determine

To evaluate $y=x^{\frac{3}{3}}$

Answer to Problem 7.3.7P

The uniqueness about this graph compared to others is that this function graphs out to be a straight line

Explanation of Solution

Given information:

The function is,

  $y=x^{\frac{3}{3}}$

Concept Used:

Function analysis.

Calculation:

The function $y=x^{\frac{3}{3}}$ was skipped because on solving,

  $y=x^{\frac{1}{1}}$

So,

  $y=x^1$

Which is,

  $y=x$

This function graphs pout to be a straight line, as shown below.

  

The uniqueness about this graph compared to others is that this function graphs out to be a straight line, whereas, other graphs gave a trivalent graph

Conclusion:The uniqueness about this graph compared to others is that this function graphs out to be a straight line