Building Functions

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What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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?

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

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How do you find the sum of two functions, (f + g)(x)?

Back

To find the sum of two functions, you add their outputs: (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

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How do you find the difference of two functions, (f - g)(x)?

Back

To find the difference of two functions, you subtract their outputs: (f - g)(x) = f(x) - g(x).

Tags

CCSS.HSF-BF.A.1B

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How do you find the product of two functions, (f * g)(x)?

Back

To find the product of two functions, you multiply their outputs: (f * g)(x) = f(x) * g(x).

Tags

CCSS.HSF-BF.A.1B

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How do you find the quotient of two functions, (f / g)(x)?

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To find the quotient of two functions, you divide their outputs: (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Tags

CCSS.HSF-BF.A.1B

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What is the composition of functions, (f ∘ g)(x)?

Back

The composition of functions is applying one function to the result of another: (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

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What is the importance of identifying the domain in function quotients?

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Identifying the domain is crucial to avoid division by zero and to ensure the function is defined for all input values.

Front

How do you evaluate a function at a specific point, such as f(g(4))?

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To evaluate f(g(4)), first find g(4), then substitute that result into f.

Tags

CCSS.HSF.IF.A.2