Function Operations and Composite Functions

Front

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

Front

What are function operations?

Back

Function operations include addition, subtraction, multiplication, and division of functions.

Tags

CCSS.HSF-BF.A.1B

Front

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

Back

The sum of two functions is found by adding their outputs: (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

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

Back

The difference of two functions is found by subtracting their outputs: (f - g)(x) = f(x) - g(x).

Tags

CCSS.HSF-BF.A.1B

Front

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

Back

The product of two functions is found by multiplying their outputs: (f ⋅ g)(x) = f(x) * g(x).

Tags

CCSS.HSF-BF.A.1B

Front

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

Back

The quotient of two functions is found by dividing their outputs: (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Tags

CCSS.HSF-BF.A.1B

Front

What is a composite function?

Back

A composite function is a function that is created by combining two functions, denoted as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

Tags

CCSS.HSF-BF.A.1C

Front

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.

Front

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.