Functions, Domain & Range

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 complete set of possible values of the independent variable (input) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output) that the function can produce.

Front

How do you determine the domain of a function from its graph?

Back

The domain can be determined by identifying all the x-values that the graph covers.

Front

How do you determine the range of a function from its graph?

Back

The range can be determined by identifying all the y-values that the graph covers.

Front

What does it mean if the domain is (-∞,+∞)?

Back

It means that the function is defined for all real numbers.

Front

What does it mean if the range is [-2,8]?

Back

It means that the output values of the function include all numbers from -2 to 8, including -2 and 8.

Front

What is an example of a function with a limited domain?

Back

f(x) = √x has a domain of [0,+∞) because you cannot take the square root of a negative number.

Front

What is an example of a function with a limited range?

Back

f(x) = x^2 has a range of [0,+∞) because the output is always non-negative.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints (e.g., (a,b)), while closed intervals do include their endpoints (e.g., [a,b]).