Rational Functions: find the domain

TL;DR

Learn how to find the domain of a rational function by ensuring the denominator is not equal to zero.

Transcript

all right in this video I'm gonna talk about how to find the domain of a function and in particular I'm going to talk about how to find the domain for a rational function first of all I'm going to review with you guys the domain of a function it's a set of all the possible X values that we can use or the possible input that we can plug it into the ... Read More

Key Insights

• 🟰 The domain of a rational function is determined by ensuring that the denominator is not equal to zero.
• 😫 When solving for the domain, set the denominator equal to zero and find the values that make the equation undefined.
• #️⃣ If the equation cannot be solved, it means the rational function has no restrictions on its domain, and the domain is all real numbers.

Questions & Answers

Q: What is the domain of a function?

The domain of a function refers to the set of all possible input values that can be used for the function.

Q: What is the key consideration when finding the domain of a rational function?

The key consideration is to ensure that the denominator of the rational function is not equal to zero.

Q: How do you find the domain of a rational function?

To find the domain, set the denominator of the rational function equal to zero and solve for the variable. The solutions to this equation are the values that cannot be in the domain.

Q: Can you provide an example of finding the domain of a rational function?

Sure! For the function f(x) = (3x - 15)/(x - 5), we set the denominator (x - 5) not equal to zero. Solving for x, we find that x cannot be equal to 5. Therefore, the domain is all real numbers except for 5.

Summary & Key Takeaways

• The domain of a function is the set of possible input values. For a rational function, the denominator must not be zero.

• To find the domain, set the denominator (bottom) of the rational function equal to zero and solve for the variable.

• If you can solve the equation, the solutions are the values that cannot be in the domain. If you cannot solve the equation, the domain is all real numbers.