1. x-intercepts

2. y-intercepts:

When x = 0, y = 0.

3. Limit as x approaches infinity:

As x → -∞,

Also, as x → +∞, y → 0

4. Domain all real x

Range [see later, in the next section].

5. Maxima and minima?

Now,

So we have a max or min at (-3, -1.5) or (3, 1.5).

Some consideration of the expression for dy/dx shows that it is

• POSITIVE for –3 < x < 3 and
• NEGATIVE for x < -3 and x > 3.

We conclude that (-3, -1.5) is the MINIMUM and (3, 1.5) is the MAXIMUM.

So the Range is -1.5 ≤ y ≤ 1.5.

Also, the slope at x = 0 is

6. Second derivative:

In this case, the second derivative may be too cumbersome to calculate quickly, and the benefits are doubtful.

So we are ready to sketch the curve: