Function Operations and Composite Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs.

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 add two functions f(x) and g(x)?

Back

To add two functions, you combine their outputs: (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

How do you subtract two functions f(x) and g(x)?

Back

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

Tags

CCSS.HSF-BF.A.1B

Front

How do you multiply two functions f(x) and g(x)?

Back

To multiply two functions, you multiply their outputs: (f ⋅ g)(x) = f(x) * g(x).

Tags

CCSS.HSF-BF.A.1B

Front

How do you divide two functions f(x) and g(x)?

Back

To divide two functions, you divide 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 formed when one function is applied to the result of another function: (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

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) for which the function is defined.