Function Operations Practice

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

How do you find 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). Remember to distribute the negative sign.

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

If f(x) = 2x + 3 and g(x) = x - 1, what is (f + g)(x)?

Back

(f + g)(x) = (2x + 3) + (x - 1) = 3x + 2.

Front

If f(x) = x^2 and g(x) = 4, what is (f - g)(x)?

Back

(f - g)(x) = x^2 - 4.

Front

What is the result of f(x) = 3x^2 + 2 and g(x) = x + 1 when finding (f - g)(x)?

Back

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

Front

How do you evaluate (f/g)(-2) if f(x) = x^2 + 1 and g(x) = x - 3?

Back

(f/g)(-2) = (f(-2) / g(-2)) = ((-2)^2 + 1) / ((-2) - 3) = 5 / -5 = -1.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.