Function Notation & Operations

Front

What is function notation?

Back

Function notation is a way to represent functions in mathematics, typically using symbols like f(x), g(x), etc., where 'f' or 'g' denotes the function and 'x' is the input variable.

Front

How do you find the sum of two functions, (f + g)(x)?

Back

To find the sum of two functions, you add their outputs: (f + g)(x) = f(x) + g(x).

Front

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

Back

To find the product of two functions, you multiply their outputs: (f ⋅ g)(x) = f(x) * g(x).

Front

How do you evaluate a function at a specific point, f(a)?

Back

To evaluate a function at a specific point, substitute the value of 'a' into the function: f(a) = replace 'x' with 'a' in f(x).

Front

What is the result of (f + g)(2) if f(x) = 3x^2 + 1 and g(x) = 4x + 5?

Back

(f + g)(2) = f(2) + g(2) = (3(2)^2 + 1) + (4(2) + 5) = 26.

Front

If f(x) = 3 and g(x) = -2x + 5, what is (f ⋅ g)(x)?

Back

(f ⋅ g)(x) = f(x) * g(x) = 3 * (-2x + 5) = -6x + 15.

Front

How do you find the sum of f(x) = -3x + 9 and g(x) = 5x - 7?

Back

f(x) + g(x) = (-3x + 9) + (5x - 7) = 2x + 2.

Front

What is the product of f(x) = 4x + 8 and g(x) = x + 3?

Back

f(x) ⋅ g(x) = (4x + 8)(x + 3) = 4x^2 + 20x + 24.

Front

If f(x) = 2x + 1, how do you find f(1)?

Back

f(1) = 2(1) + 1 = 3.

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.