Function Notation & Composite Functions Flashcard

Front

What is function notation?

Back

Function notation is a way to represent functions in mathematics, typically written as f(x), where 'f' is the name of the function and 'x' is the input variable.

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function's equation. For example, if f(x) = 2x + 3, then f(4) = 2(4) + 3 = 11.

Front

What is a composite function?

Back

A composite function is formed when one function is applied to the result of another function, denoted as (f∘g)(x) = f(g(x)).

Front

How do you find (f∘g)(x) if f(x) = 2x and g(x) = x + 1?

Back

To find (f∘g)(x), first find g(x) = x + 1, then substitute into f: f(g(x)) = f(x + 1) = 2(x + 1) = 2x + 2.

Front

What is the value of g(-4) if g(x) = 3 - x?

Back

g(-4) = 3 - (-4) = 3 + 4 = 7.

Front

How do you find f(6) for the function f(x) = 3x - 8?

Back

Substitute 6 into the function: f(6) = 3(6) - 8 = 18 - 8 = 10.

Front

What is the output of g(25) if g(x) = 6x - 19?

Back

g(25) = 6(25) - 19 = 150 - 19 = 131.

Front

If f(x) = 3x + 10 and g(x) = x - 2, what is g(f(-10))?

Back

First find f(-10): f(-10) = 3(-10) + 10 = -30 + 10 = -20. Then find g(-20): g(-20) = -20 - 2 = -22.

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

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.