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 limited domain because x cannot be 0.

Front

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

Back

The function f(x) = x^2 has a limited range of y ≥ 0, since squares of real numbers cannot be negative.

Front

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

Back

The domain is x ≥ 3, because 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 y ≤ 0, since the function produces only non-positive values.

Front

What is a real-world example of domain and range?

Back

In a function that models the height of a ball thrown in the air, the domain could be the time (in seconds) the ball is in the air, and the range would be the height of the ball at those times.

Front

What does it mean if a function is defined for all real numbers?

Back

It means the domain of the function includes every possible real number, often represented as (-∞, ∞).