How to Find the Domain of a Rational Function

TL;DR

This video explains how to find the domain for rational functions by setting the denominator equal to zero and excluding those values from the domain.

Transcript

in this video we're going to talk about how to find the domain for rational functions so domain for rational functions rational functions so a rational function is a function that's a fraction and it's basically a polynomial over a polynomial so things like you know x squared plus 4 over X minus 6 that's a rational function you have powers of X her... Read More

Key Insights

• ❓ A rational function is a fraction with polynomials as the numerator and denominator.
• 😫 To find the domain for rational functions, set the denominator equal to zero and solve for x.
• 0️⃣ Excluding values that make the denominator zero is necessary because dividing by zero is undefined.
• 😑 The domain for a rational function can be expressed using set builder notation.
• 🥺 Cancelling out common factors in rational functions before finding the domain can lead to the wrong answer.
• 😫 The domain of a rational function is the set of all x values except for the ones found by setting the denominator equal to zero.
• 0️⃣ Rational functions may have multiple values that make the denominator zero, requiring careful consideration of all solutions.

Questions & Answers

Q: What is a rational function?

A rational function is a fraction with polynomials as the numerator and denominator.

Q: How do you find the domain for rational functions?

To find the domain, set the denominator equal to zero and solve for x. Exclude the values found in this step from the domain.

Q: Why is it important to exclude values that make the denominator zero from the domain?

Excluding values that make the denominator zero is important because dividing by zero is undefined and results in infinite values.

Q: Can the domain for rational functions be written using set builder notation?

Yes, the domain can be written in set builder notation as the set of all x such that x is not equal to the values that make the denominator zero.

Summary & Key Takeaways

• Rational functions are fractions with polynomials as numerators and denominators.

• To find the domain for rational functions, set the denominator equal to zero and solve for x.

• The domain is all values of x except for the ones found in step one.