Domain and Range of Functions

Front

What is the definition of the domain of a function?

Back

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

Front

What is the definition of the range of a function?

Back

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

Front

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

Back

The domain can be determined by identifying the x-values for which the graph exists, including any restrictions such as holes or vertical asymptotes.

Front

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

Back

The range can be determined by identifying the y-values that the graph reaches, including any restrictions such as horizontal asymptotes.

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 square of any real number is non-negative.

Front

What is the domain of the function f(x) = 1/(x - 3)?

Back

The domain is all real numbers except x = 3, where the function is undefined.

Front

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

Back

The range is [-1, 1], as the sine function oscillates between -1 and 1.

Front

How do you find the range of a set of ordered pairs?

Back

The range can be found by listing all the unique y-values from the ordered pairs.

Front

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

Back

The domain is x > 0, since the logarithm is only defined for positive numbers.