First, judge the function value of negative infinity. If it is positive, go from top to bottom; if it is negative, go from bottom to top;

Arrange all zeros of the function in order from small to large;

Then penetrate the root: odd roots bounce back through even roots (single root, three roots, etc. Pass through the number axis, and the two roots do not pass through the number axis);

Finally, the positive and negative function values of each interval are judged.

Example:

f(x)=(x+ 1)(x-2)(x-2)(x-6)

When x is negative infinity, it is the fourth power of x, which is positive, so it passes through the number axis;

List all zeros:-1, 2, 2, 6 (where 2 is a double root, please pay attention to the rebound when penetrating the root);

Passing through the number axis from above, passing through the number axis to below when reaching-1, touching the number axis at 2 o'clock but not passing through (bouncing back), still below the number axis, and passing through the number axis to above when reaching 6 o'clock;

So the interval with positive function value is: (negative infinity,-1), (6, positive infinity).

The interval with negative function value is: (-1, 2), (2, 6).