Domain and Range

Front

What is the definition of 'Domain' in a function?

Back

The set of all possible input values (x-values) for which the function is defined.

Front

What is the definition of 'Range' in a function?

Back

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

Front

What does it mean if a graph has a minimum value?

Back

It means that there is a lowest point on the graph, and the function does not go below this value.

Front

What does it mean if a graph has a maximum value?

Back

It means that there is a highest point on the graph, and the function does not exceed this value.

Front

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

Back

Identify the lowest and highest points on the graph and express the range in interval notation or inequality.

Front

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

Back

y ≥ 0, since the minimum value of x^2 is 0.

Front

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

Back

All real numbers except x = 0, since the function is undefined at x = 0.

Front

How can you express the range of a function that is always increasing?

Back

The range is typically from the minimum value to infinity.

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 values.

Front

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

Back

y ≤ 0, since the maximum value is 0 and the function decreases without bound.