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 is function notation?

Back

Function notation is a way to denote functions using symbols, typically in the form f(x), where f represents the function and x is the input variable.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Front

What is the composition of functions?

Back

The composition of functions is an operation that takes two functions f and g and produces a new function (g ∘ f)(x) = g(f(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 the function g. This means replacing every instance of x in g with f(x).

Tags

CCSS.HSF-BF.A.1C

Front

What is the difference between f(x) + g(x) and f(x) ⋅ g(x)?

Back

f(x) + g(x) is the sum of the two functions, while f(x) ⋅ g(x) is the product of the two functions.

Tags

CCSS.HSF-BF.A.1B

Front

What is the formula for the sum of two functions?

Back

The sum of two functions f and g is given by (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

What is the formula for the difference of two functions?

Back

The difference of two functions f and g is given by (f - g)(x) = f(x) - g(x).

Tags

CCSS.HSF-BF.A.1B

Front

What is the formula for the product of two functions?

Back

The product of two functions f and g is given by (f ⋅ g)(x) = f(x) ⋅ g(x).

Tags

CCSS.HSF-BF.A.1B

Front

What is the formula for the quotient of two functions?

Back

The quotient of two functions f and g is given by (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Tags

CCSS.HSF-BF.A.1B

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants.