Operations and Composition of Functions

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What is a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Tags

CCSS.8.F.A.1

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What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

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What does it mean to perform operations on functions?

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Performing operations on functions involves combining two or more functions using addition, subtraction, multiplication, or division.

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CCSS.HSF-BF.A.1B

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How do you add two functions?

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To add two functions f(x) and g(x), you compute (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

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How do you subtract two functions?

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To subtract two functions f(x) and g(x), you compute (f - g)(x) = f(x) - g(x).

Tags

CCSS.HSF-BF.A.1B

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How do you multiply two functions?

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To multiply two functions f(x) and g(x), you compute (f * g)(x) = f(x) * g(x).

Tags

CCSS.HSF-BF.A.1B

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How do you divide two functions?

Back

To divide two functions f(x) and g(x), you compute (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Tags

CCSS.HSF-BF.A.1B

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What is function composition?

Back

Function composition is the process of applying one function to the results of another function, denoted as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

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How do you find f(g(x))?

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To find f(g(x)), substitute g(x) into the function f wherever x appears.

Tags

CCSS.HSF-BF.A.1C