What is the domain of a function? | Functions | Algebra I | Khan Academy | Summary and Q&A

TL;DR

A function's domain is the set of all inputs over which it is defined, excluding any undefined values.

Key Insights

• 🥡 A function takes inputs and produces outputs, known as f(x).
• 😫 The domain of a function is the set of all inputs for which the function has defined outputs.
• 🥺 Some functions have undefined outputs for specific inputs, leading to restrictions in the domain.

Transcript

Read and summarize the transcript of this video on Glasp Reader (beta).

Questions & Answers

Q: What is the definition of a function and how does it relate to inputs and outputs?

A function takes inputs and produces outputs. The input is denoted as x, and the output is denoted as f(x).

Q: How do you determine the output of a function for a given input?

To find the output of a function for a specific input, substitute the input value into the function's definition. For example, for the function f(x) = 2/x, inputting 3 would give an output of 2/3.

Q: What happens when an input of 0 is used for a function?

The function's definition may not provide a clear output for an input of 0. In such cases, the function is undefined for that input, and the domain excludes 0.

Q: How is the domain of a function defined?

The domain of a function is the set of all valid inputs for which the function has defined outputs. It may be restricted by certain conditions or exclusions.

Summary & Key Takeaways

• A function takes inputs and produces outputs, where the output is called f(x).

• The domain of a function is the set of all inputs for which the function has defined outputs.

• Some functions have undefined outputs for specific inputs, leading to restrictions in the domain.