Given the following function

graph the three functions **y = f(x), y = f(-x),** and **y = -f(-x)** and see if any two of the graphs coincide.

Using Derive,

- Prepare the program for graphics.
- If the first menu item is
*Algebra*then press . - Press for
*Author*. - Enter the function
f(x) := sin(x) + 4x^3 - Press twice to get the graph. Note the color of the graph.
- Press twice and enter
f(-x) - Press twice to get the graph. Again note the color of the graph.
- Press twice and enter
-f(-x) - Press twice to get the graph. Again note the color of the graph.

It appears from the drawing of the latter graph that the two functions **y =
f(x)** and **y = -f(-x)** are the same. Hence, it appears that the
function **y = f(x)** is odd.