Domain and Range (Shortened Version)

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 'All real numbers' as its domain?

Back

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

Front

If a graph shows the range as -3 ≤ y < 1, what does this indicate?

Back

The output values (y-values) of the function are between -3 and 1, including -3 but not including 1.

Front

How do you determine the domain from a graph?

Back

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

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

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

Back

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

Front

If a function is defined as f(x) = 1/(x-2), what is its domain?

Back

The domain is all real numbers except x = 2, where the function is undefined.

Front

What does the notation -4 ≤ x ≤ 3 represent?

Back

It indicates that x can take any value from -4 to 3, including both endpoints.

Front

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

Back

The range is -1 ≤ y ≤ 1, as the sine function oscillates between -1 and 1.