Evaluating and Composition of Functions

Front

Define a function.

Back

A function is a relation that assigns exactly one output for each input from a set of inputs, typically represented as f(x).

Front

What is function evaluation?

Back

Function evaluation is the process of finding the output of a function for a specific input value.

Front

Evaluate f(x) = 2x + 3 for f(4).

Back

f(4) = 2(4) + 3 = 8 + 3 = 11.

Front

What is the composition of functions?

Back

The composition of functions is the process of applying one function to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

Find f(g(2)) if f(x) = x^2 and g(x) = x + 1.

Back

g(2) = 2 + 1 = 3; f(g(2)) = f(3) = 3^2 = 9.

Front

Evaluate g(x) = 3x - 5 for g(-1).

Back

g(-1) = 3(-1) - 5 = -3 - 5 = -8.

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

Evaluate f(x) = |x - 4| for f(2).

Back

f(2) = |2 - 4| = |-2| = 2.

Front

If f(x) = x + 2 and g(x) = 2x, find (f ∘ g)(3).

Back

g(3) = 2(3) = 6; f(g(3)) = f(6) = 6 + 2 = 8.

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.