Domain and Range of Functions

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

Given the function f(x) = x^2, what is the domain?

Back

The domain is all real numbers, represented as (-∞, ∞).

Front

Given the function f(x) = x^2, what is the range?

Back

The range is all real numbers greater than or equal to 0, represented as [0, ∞).

Front

What does it mean if a function is not defined for certain x-values?

Back

It means those x-values are not included in the domain of the function.

Front

How do you find the domain of a function from a graph?

Back

Identify the x-values for which the graph exists; these values make up the domain.

Front

How do you find the range of a function from a graph?

Back

Identify the y-values that the graph reaches; these values make up the range.

Front

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

Back

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

f(x) = sin(x) has a range of [-1, 1].

Front

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

Back

The domain is [1, ∞) because the expression under the square root must be non-negative.