Composition of Functions & Function Operations

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean to compose functions?

Back

Composing functions means applying one function to the result of another function, denoted as f(g(x)).

Front

How do you find f(g(x))?

Back

To find f(g(x)), first evaluate g(x) and then substitute that result into f.

Front

What is the notation for function operations?

Back

Function operations can be denoted as f(x) + g(x), f(x) - g(x), f(x) * g(x), and f(x) / g(x).

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.

Front

How do you find the radius of a circle from its equation?

Back

In the equation (x-h)² + (y-k)² = r², the radius r is the square root of the constant on the right side.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions do not have a constant rate of change and can graph as curves.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function; if any vertical line intersects the curve more than once, it is not a function.

Front

How do you evaluate g(5) if g(x) = 4x + 1?

Back

Substitute 5 into the function: g(5) = 4(5) + 1 = 20 + 1 = 21.