Domain and Range

Front

What is the definition of Domain in mathematics?

Back

The domain of a function is the complete set of possible values of the independent variable (usually x) for which the function is defined.

Front

What is the definition of Range in mathematics?

Back

The range of a function is the complete set of possible values of the dependent variable (usually y) that results from using the function.

Front

How do you find the domain of a function?

Back

To find the domain, identify all the values of x that can be input into the function without causing any mathematical errors (like division by zero or taking the square root of a negative number).

Front

How do you find the range of a function?

Back

To find the range, determine all the possible output values (y-values) that the function can produce based on its domain.

Front

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

Back

The function f(x) = 1/x has a domain of all real numbers except x = 0.

Front

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

Back

The function f(x) = x^2 has a range of all real numbers greater than or equal to 0.

Front

What is the domain of the function f(x) = √(x - 3)?

Back

The domain is x ≥ 3, since the expression under the square root must be non-negative.

Front

What is the range of the function f(x) = -x^2?

Back

The range is all real numbers less than or equal to 0, since the function opens downwards.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements, meaning each y-value corresponds to exactly one x-value.

Front

How can you determine if a function is one-to-one?

Back

You can use the horizontal line test: if any horizontal line intersects the graph of the function more than once, the function is not one-to-one.