Domain and Range

Front

What is the definition of 'Domain' in mathematics?

Back

The set of all possible input values (x-values) for a function.

Front

What is the definition of 'Range' in mathematics?

Back

The set of all possible output values (y-values) for a function.

Front

What does it mean if a function has a domain of all real numbers?

Back

It means that any real number can be used as an input for the function.

Front

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

Back

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

Front

What is the range of a function?

Back

The range is the set of all output values (y-values) that a function can produce.

Front

If a function's graph goes up to a maximum y-value of 3, what is the range?

Back

The range is all y-values from the minimum to the maximum, e.g., [-1, 3].

Front

What does the notation (-∞, ∞) represent?

Back

It represents all real numbers, indicating that there are no restrictions on the domain or range.

Front

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

Back

The domain is x ≥ 1, since the expression under the square root must be non-negative.

Front

If a function is defined only for x-values between -2 and 2, what is its domain?

Back

The domain is [-2, 2].

Front

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

Back

The range is [0, ∞) because the output is always non-negative.