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) that will not cause any undefined behavior in the function.

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 result 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 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) that the function can produce based on its domain.

Front

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

Back

The function f(x) = √(x - 1) has a restricted domain of x ≥ 1 because the expression under the square root must be non-negative.

Front

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

Back

The function f(x) = 1/x has a range of all real numbers except 0, since it can never output a value of 0.

Front

What is the domain of the function f(x) = 1/(x - 2)?

Back

The domain is all real numbers except x = 2, because the function is undefined at that point.

Front

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

Back

The range is all real numbers greater than or equal to 0, since a square of a real number cannot be negative.

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 output is unique.

Front

How can you determine if a function is one-to-one using the horizontal line test?

Back

If any horizontal line intersects the graph of the function more than once, the function is not one-to-one.