Chapter 1, Problem 38RE

Solution

To sketch: The graph of the given function.

The graph of the given function is below:

  

Given information:

Consider the given function.

  $y=\sin x-x^3$

Calculation:

Consider the given function.

  $y=\sin x-x^3$

Draw the graph of the given function $y=\sin x-x^3$:

  

Now, check it is even, odd and neither even or nor.

Replace $x$ by $-x$ :

  $\begin{array}{c}y=\sin \left(-x\right)-{\left(-x\right)}^3\\ y=-\sin x+x^3\\ y=-\left(\sin x-x^3\right)\\ y=-y\end{array}$

Therefore, the given function is odd function.