Multiplying Functions

Front

What is the definition of multiplying functions?

Back

Multiplying functions involves taking two functions, f(x) and g(x), and creating a new function h(x) = f(x) * g(x).

Front

If f(x) = x + 2 and g(x) = 3x, what is f(x) ⋅ g(x)?

Back

f(x) ⋅ g(x) = (x + 2)(3x) = 3x^2 + 6x.

Front

What is the distributive property in multiplication of functions?

Back

The distributive property states that a(b + c) = ab + ac. This applies to functions as well: f(x)(g(x) + h(x)) = f(x)g(x) + f(x)h(x).

Front

If f(x) = 2x and g(x) = x^2, what is f(x) ⋅ g(x)?

Back

f(x) ⋅ g(x) = (2x)(x^2) = 2x^3.

Front

What is the result of multiplying a constant function by a variable function?

Back

If f(x) = k (a constant) and g(x) = x, then f(x) ⋅ g(x) = kx.

Front

If f(x) = x^2 and g(x) = x + 1, what is f(x) ⋅ g(x)?

Back

f(x) ⋅ g(x) = (x^2)(x + 1) = x^3 + x^2.

Front

What is the product of two linear functions?

Back

If f(x) = ax + b and g(x) = cx + d, then f(x) ⋅ g(x) = (ax + b)(cx + d) = acx^2 + (ad + bc)x + bd.

Front

If f(x) = 4 and g(x) = x + 3, what is f(x) ⋅ g(x)?

Back

f(x) ⋅ g(x) = 4(x + 3) = 4x + 12.

Front

What is the degree of the product of two polynomial functions?

Back

The degree of the product of two polynomial functions is the sum of their degrees. If f(x) has degree m and g(x) has degree n, then h(x) = f(x) * g(x) has degree m + n.

Front

If f(x) = x^3 - 3x and g(x) = -4x + 1, what is f(x) ⋅ g(x)?

Back

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