Domain and Range

What is the definition of 'Domain' in mathematics?

• The range of values that a function can output.

• The complete set of possible values of the independent variable (usually x) for which the function is defined.

• The maximum value that a function can reach.

• The minimum value that a function can reach.

What is the domain of the function @@f(x) = x^2 - 4@@?

• All real numbers, written as @@(- ext{∞}, ext{∞})@@

• Only positive real numbers, written as @@[0, ext{∞})@@

• Only negative real numbers, written as @@(- ext{∞}, 0)@@

• All integers, written as @@ ext{Z}@@

What is the definition of 'Range' in mathematics?

• The range of a function is the complete set of possible values of the dependent variable (usually y) that result from using the function.

• The range of a function is the difference between the highest and lowest values of the independent variable.

• The range of a function is the set of all possible input values (usually x) that can be used in the function.

• The range of a function is the average of all the output values of the function.

What is the range of the function @@f(x) = ext{sin}(x)@@?

• All real numbers

• [-1, 1]

• [0, 1]

• (-1, 1)

How do you determine the domain of a function?

• Identify all the values of x that can be input into the function without causing any mathematical errors (like division by zero or taking the square root of a negative number).

• Choose any value of x, as all values are valid for the domain.

• The domain is always all real numbers unless specified otherwise.

• The domain is determined by the range of the function.

What is the domain of the function @@f(x) = ext{tan}(x)@@?

• All real numbers

• All real numbers except for @@x = rac{ ext{π}}{2} + n ext{π}@@, where n is any integer

• Only integers

• All real numbers except for @@x = n ext{π}@@, where n is any integer

What is the domain of the function @@f(x) = ext{sqrt}(x - 1)@@?

• All real numbers

• All real numbers greater than 0

• All real numbers greater than or equal to 1

• All real numbers less than or equal to 1

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

• All real numbers

• All real numbers greater than 0

• All real numbers greater than or equal to 0

• All real numbers less than or equal to 0

What is the range of the function @@f(x) = ext{tan}(x)@@?

• All real numbers, written as @@(- ext{∞}, ext{∞})@@

• Only positive real numbers, written as @@[0, ext{∞})@@

• Only negative real numbers, written as @@(- ext{∞}, 0)@@

• All integers, written as @@ ext{Z}@@

What is the range of the function @@f(x) = ext{log}(x)@@?

• All positive numbers, written as @@(0, ext{∞})@@

• All real numbers, written as @@(- ext{∞}, ext{∞})@@

• All negative numbers, written as @@(- ext{∞}, 0)@@

• All integers, written as @@ ext{Z}@@