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
Let's have a little bit of a review of what a function is before we talk about what it means that what the domain of a function means. So function we can view as something -- so I put a function in this box here and it takes inputs, and for a given input, it's going to produce an output which we call f of x. So, for example, let's say that we have ... Read More
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
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A function takes inputs and produces outputs, where the output is called f(x).
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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.