Function Operations

Front

What is function addition?

Back

Function addition is the operation of adding two functions together. If f(x) and g(x) are two functions, then their sum is defined as (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

Given f(n)=n^2+4n and g(n)=-n-5, find f(n)+g(n).

Back

f(n) + g(n) = n^2 + 4n - n - 5 = n^2 + 3n - 5.

Tags

CCSS.HSF-BF.A.1B

Front

What is function composition?

Back

Function composition is the operation of applying one function to the results of another function. If f(x) and g(x) are two functions, then the composition is defined as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

Given f(x) = x^2 + x and g(x) = 3x + 1, find f(g(4)).

Back

f(g(4)) = f(13) = 13^2 + 13 = 182.

Tags

CCSS.HSF-BF.A.1C

Front

What is function multiplication?

Back

Function multiplication is the operation of multiplying two functions together. If f(x) and g(x) are two functions, then their product is defined as (f * g)(x) = f(x) * g(x).

Tags

CCSS.HSF-BF.A.1B

Front

Given f(n)=2n+1 and g(n)=3n, find f(n)+g(n).

Back

f(n) + g(n) = 2n + 1 + 3n = 5n + 1.

Tags

CCSS.HSF-BF.A.1B

Front

What is the difference between function addition and function multiplication?

Back

Function addition combines the outputs of two functions, while function multiplication combines the outputs by multiplying them together.

Tags

CCSS.HSF-BF.A.1B

Front

Given f(x)=x^3-3x and g(x)=-4x+1, find f(x)*g(x).

Back

f(x) * g(x) = (x^3 - 3x)(-4x + 1) = -4x^4 + x^3 + 12x^2 - 3x.

Tags

CCSS.HSF-BF.A.1B

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

Given f(x)=2x+4 and g(x)=3x^2-1, find f(x)*g(x).

Back

f(x) * g(x) = (2x + 4)(3x^2 - 1) = 6x^3 + 12x^2 - 2x - 4.

Tags

CCSS.HSF-BF.A.1B