Building Functions

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 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 sum of two functions, (f + g)(x)?

Back

To find the sum of two functions, you add their outputs: (f + g)(x) = f(x) + g(x).

Front

How do you find the difference of two functions, (f - g)(x)?

Back

To find the difference of two functions, you subtract their outputs: (f - g)(x) = f(x) - g(x).

Front

How do you find the product of two functions, (f * g)(x)?

Back

To find the product of two functions, you multiply their outputs: (f * g)(x) = f(x) * g(x).

Front

How do you find the quotient of two functions, (f / g)(x)?

Back

To find the quotient of two functions, you divide their outputs: (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Front

What is the composition of functions, (f ∘ g)(x)?

Back

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

Front

What is the importance of identifying the domain in function quotients?

Back

Identifying the domain is crucial to avoid division by zero and to ensure the function is defined for all input values.

Front

How do you evaluate a function at a specific point, such as f(g(4))?

Back

To evaluate f(g(4)), first find g(4), then substitute that result into f.