Sketching graphs of polynomial functions are useful in graphing techniques, and solving inequalities.

**Steps**

1. First mark down the roots of the polynomial function.

2. Decide how the tail ends behave, whether it is above or below the X axis. This can be determined from the coef of the highest power. For instance, if the polynomial is of degree 6 and the coef of the highest power is positive, then when X approaches either positive or negative infinity, the function approaches positive infinity, so the tail ends are above the X axis.

3. Determine how the function behaves at the roots. When there are 3 or more odd number of roots at the same point, there is a point of inflexion at the root. When there are 2 or more even number of roots at the same point, there is a minimum or maximum point at the root.

**Example 1**

**Example 2**

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