Main things you need to know on finding the domain of a rational function

The video tutorial explains how to find the domain of rational functions by setting the denominator equal to zero, as this identifies values that make the function undefined. It covers methods like factoring and inverse operations to solve for these values. The tutorial also discusses discontinuities, such as holes and asymptotes, and emphasizes the importance of understanding these concepts to avoid common mistakes. The video aims to clarify misconceptions and provide a comprehensive understanding of domain restrictions in rational functions.

What is the first step in finding the domain of a rational function?

• Set the denominator equal to zero

• Simplify the expression

• Find the range of the function

• Set the numerator equal to zero

Why is it important to set the denominator equal to zero when finding the domain?

• To find the maximum value of the function

• To simplify the expression

• To identify values that make the function undefined

• To find the range of the function

When factoring a quadratic expression in the denominator, what should you remember to include?

• Only positive solutions

• Only negative solutions

• Both positive and negative solutions

• No solutions

What is a removable discontinuity in a rational function?

• A point where the function has a horizontal asymptote

• A point where the function has a vertical asymptote

• A point where the function is undefined but can be simplified

• A point where the function is defined

What should you do before simplifying a rational expression to find its domain?

• Factor the numerator

• Set the denominator equal to zero

• Set the numerator equal to zero

• Factor the denominator

What is a common mistake when dealing with rational expressions?

• Setting the numerator equal to zero

• Only factoring the numerator

• Ignoring the numerator

• Assuming all terms can be divided out

Why might a rational expression have no restrictions on its domain?

• The numerator is zero

• The expression is already simplified

• The expression has a hole

• The denominator is a constant

What should you check for in the original expression before simplifying?

• The range of the function

• The degree of the polynomial

• The values that make the denominator zero

• The values that make the numerator zero

What is a misconception about rational expressions?

• They always have a hole

• They always have a discontinuity

• They always have a vertical asymptote

• They always have a horizontal asymptote

What is the domain of a rational function with a constant denominator?

• All real numbers

• All positive numbers

• All negative numbers

• No numbers