Chapter 9, Problem 2E

To determine

To calculate:To find the equation that represents the below graph -

  

Answer to Problem 2E

The answer is $H.$$y=-\frac{1}{2}{x}^3$

Explanation of Solution

Given information:

Given graph is -

  

Calculation:

Given the graph is

  

From the graph, we can see that,

for $x=0$ , $y=0$ ,

For $x=1$ , $y=-0.5$

For $x=-1$ , $y=0.5$

Putting these values of $x$ and $y$ in the below equations −

  $y=2^x-1$

  $y=-2^x$

  $y=-\frac{1}{2}{x}^3$

  $y=\frac{1}{2}{x}^3$

The third equation satisfies all the values.

Thus, the equation of the given graph is $y=-\frac{1}{2}{x}^3$

Conclusion:

The answer is $H.$$y=-\frac{1}{2}{x}^3$