How to determine the domain of a rational function - domain and range

The video tutorial explains how to find the domain of rational functions, particularly when a root is in the denominator. It covers the concept of domain, using examples like 3/X and 1/sqrt(X-3), and discusses how to handle division by zero and square roots. The tutorial also demonstrates solving inequalities to determine valid input values for the function.

What happens to the domain of a function if the denominator becomes zero?

• The function remains unchanged.

• The function becomes infinite at that point.

• The function becomes zero at that point.

• The function becomes undefined at that point.

Why can't we take the square root of a negative number in the context of real numbers?

• Because it results in a negative number.

• Because it results in zero.

• Because it results in a complex number.

• Because it results in an undefined value.

For the function 1/sqrt(X-3), what value of X makes the denominator zero?

• X = 1

• X = -3

• X = 3

• X = 0

What is the domain of the function 1/sqrt(X-3)?

• All numbers greater than 3

• All numbers except X = 3

• All numbers less than 3

• All real numbers

Why must the expression inside the square root in the denominator be greater than zero?

• To ensure the function is zero.

• To ensure the function is defined.

• To ensure the function is negative.

• To ensure the function is positive.