Chapter 3.1, Problem 2CFU

To determine

To explain: Rotating a graph of an odd function ${180}^{\circ }$ will affect its appearance. Draw an example.

Explanation of Solution

Given information: Rotating a graph of an odd function ${180}^{\circ }$

Calculation:

If you rotate the intercept ${180}^{\circ }$ it will still be the same.

It will still run through the origin or at least parallel with it.

When you rotate it the direction becomes inverted.

When it was rising it will now be decreasing and vice versa.

It maintains the same intercept and symmetry.

It’s still an odd function.

This is a steep function that comes from the down-left part close to the origin. It hits the x-axis just before the origin and then goes straight left on the x-axis to the origin. It then continuous straight left and about at the same length you hit the x-axis it takes off upwards and it’s again steep. Try to maintain symmetry.

To draw take the $y=x^3$ function.

Now it comes from the upper-left part. It hits the x-axis again, straight through the origin and then goes downward. The two functions combined look like an hourglass.

Then rotate the function.

Thus, it will still be an odd function and the direction is inverted.