EXIT TICKET Composite Functions

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, where the output of one function becomes the input of the other. It is denoted as (g ∘ f)(x) = g(f(x)).

Front

How do you denote the composition of two functions f and g?

Back

The composition of two functions f and g is denoted as g(f(x)) or (g ∘ f)(x).

Front

Given f(x) = 4x - 3 and g(x) = x^2 - 4, how do you find g(f(x))?

Back

To find g(f(x)), substitute f(x) into g. First, calculate f(x) = 4x - 3, then replace x in g(x) with f(x): g(f(x)) = g(4x - 3) = (4x - 3)^2 - 4.

Front

What is the result of g(f(x)) when f(x) = 4x - 3 and g(x) = x^2 - 4?

Back

The result is g(f(x)) = 16x^2 - 24x + 5.

Front

What is the first step in finding the composition of two functions?

Back

The first step is to evaluate the inner function, which is the function that is applied first.

Front

What is the significance of the order of functions in composition?

Back

The order of functions in composition matters because (g ∘ f)(x) is not necessarily equal to (f ∘ g)(x). The output depends on which function is applied first.

Front

How do you simplify the expression (4x - 3)^2 - 4?

Back

To simplify (4x - 3)^2 - 4, first expand (4x - 3)^2 to get 16x^2 - 24x + 9, then subtract 4 to get 16x^2 - 24x + 5.

Front

What is the domain of a composite function?

Back

The domain of a composite function g(f(x)) is the set of all x in the domain of f such that f(x) is in the domain of g.

Front

What is the range of a composite function?

Back

The range of a composite function g(f(x)) is the set of all possible output values of g(f(x)) as x varies over the domain of f.

Front

Can composite functions be used to model real-world situations?

Back

Yes, composite functions can be used to model real-world situations where one quantity depends on another, such as in physics, economics, and biology.