Alg2 Operations on Functions

Front

What is the sum of two functions f(x) and g(x)?

Back

The sum of two functions f(x) and g(x) is defined as (f + g)(x) = f(x) + g(x).

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f + g)(x).

Back

(f + g)(x) = 5x^2 + 6x - 1.

Front

What is the quotient of two functions f(x) and g(x)?

Back

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

Front

Given f(x) = 3x^2 + 4x - 5 and g(x) = 2x + 9, find f(x) / g(x).

Back

f(x) / g(x) = \frac{3x^2 + 4x - 5}{2x + 9}.

Front

What is the product of two functions f(x) and g(x)?

Back

The product of two functions f(x) and g(x) is defined as (f ⋅ g)(x) = f(x) * g(x).

Front

Given f(x) = 4x + 8 and g(x) = x + 3, find (f ⋅ g)(x).

Back

(f ⋅ g)(x) = 4x^2 + 20x + 24.

Front

What is the difference of two functions f(x) and g(x)?

Back

The difference of two functions f(x) and g(x) is defined as (f - g)(x) = f(x) - g(x).

Front

Given f(x) = x^2 - 9 and g(x) = x + 3, find (f / g)(x).

Back

(f / g)(x) = x - 3.

Front

What is the definition of a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable x in the polynomial expression.