Question

Name three functions that are continuous at every real number.

Short answer

The three functions that are continuous at every real number are sine, cosine function, and polynomial functions.

Step-by-step solution

Step 1. Given Information 

A continuous function is defined as a function that doesn't have discontinuities and the graph of the function is continuous without any break or jump.

Real numbers are numbers that include whole numbers, natural numbers, integers, and both rational and irrational numbers.

Step 2. Stating three functions that are continuous at every real number

The polynomial functions are continuous at every real number.

The sine and cosine functions are continuous at every real number because we get the same value if we approached from the left-hand side or right-hand side.