Domain and Range Practice

Front

What is the definition of Domain in a function?

Back

The domain of a function is the complete set of possible values of the independent variable (usually x) that will not cause any undefined behavior in the function.

Front

What is the definition of Range in a function?

Back

The range of a function is the complete set of possible values of the dependent variable (usually y) that the function can produce.

Front

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

Back

To determine the domain from a graph, identify all the x-values for which the graph has points. The domain is the set of these x-values.

Front

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

Back

To determine the range from a graph, identify all the y-values that the graph reaches. The range is the set of these y-values.

Front

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

Back

The domain is all real numbers except x = 0, since division by zero is undefined.

Front

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

Back

The range is all real numbers y such that y ≥ 0, since a square of a real number cannot be negative.

Front

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

Back

The domain is all real numbers x such that x ≥ 0, since the square root of a negative number is undefined.

Front

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

Back

The range is all real numbers, since as x takes all real values, -x will also take all real values.

Front

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

Back

The domain is all real numbers x such that x > 0, since the logarithm of zero or a negative number is undefined.

Front

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

Back

The range is all real numbers y such that -1 ≤ y ≤ 1, since the sine function oscillates between -1 and 1.