Question

The graph of a polynomial function is always smooth and continuous. Name a function studied earlier that is smooth and not continuous. Name one that is continuous but not smooth.

Short answer

The function which is continuous but not smooth is the Greatest Integer Function.

A function that is smooth but not continuous is the Modulus function.

Step-by-step solution

Step 1. Given information

The graph of a polynomial function is always smooth and continuous. We have to name a function studied earlier that is smooth and not continuous and one that is continuous but not smooth.

Step 2. Functions example

The function which is continuous but not smooth is the Greatest Integer Function.

A function that is smooth but not continuous is the Modulus function.