Domain & Range

Front

What is the definition of 'domain' in 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 'range' in 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 given its equation?

Back

To determine the domain, identify any restrictions on the input values, such as division by zero or square roots of negative numbers.

Front

How do you determine the range of a function given its equation?

Back

To determine the range, analyze the output values produced by the function, considering any restrictions based on the function's behavior.

Front

What is the domain of the function f(x) = 1/(x-2)?

Back

The domain is all real numbers except x = 2, since the function is undefined at that point.

Front

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

Back

The range is all real numbers greater than or equal to 0, since the output of x^2 is never 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 is only defined for non-negative numbers.

Front

What is the range of the function f(x) = 3x + 1?

Back

The range is all real numbers, since a linear function can produce any output value.

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 is only defined for positive numbers.

Front

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

Back

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