Composition with Tables and Graphs

Front

What is a function in mathematics?

Back

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

Front

Define the composition of functions.

Back

The composition of functions f and g, denoted as (f ∘ g)(x), is defined as f(g(x)).

Front

Evaluate the composition of functions: g(f(4)) if f(4) = 2 and g(2) = 3.

Back

g(f(4)) = g(2) = 3.

Front

What is the formula to calculate the total cost including tax?

Back

Total Cost = Price + (Price × Tax Rate).

Front

If a pizza shop charges $3.00 per slice, what is the cost for 4 slices?

Back

Cost for 4 slices = 4 × $3.00 = $12.00.

Front

How do you calculate the total price after a 10% tax on a $20 purchase?

Back

Total Price = $20 + ($20 × 0.10) = $22.00.

Front

What does the notation g(f(x)) represent?

Back

It represents the composition of function g with function f, where f is applied first and then g is applied to the result.

Front

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

Back

f(3) = 2(3) + 1 = 7.

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.