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's domain is 'x ≥ 0'?

Back

The function is defined for all x-values starting from 0 and extending to positive infinity.

Front

What does it mean if a function's range is '[1, ∞)'?

Back

The output values of the function start from 1 and extend to positive infinity.

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

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

Back

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

Front

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

Back

x ≥ 0, since the square root function is only defined for non-negative numbers.

Front

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

Back

y ≥ 0, since the output of the square root function is always non-negative.

Front

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

Back

All real numbers except x = 0, since division by zero is undefined.

Front

What is the range of the function f(x) = 1/x?

Back

All real numbers except y = 0, since the function never outputs zero.