Understanding Range and Domain

What is the definition of the domain of a function?

• The domain of a function is the set of all possible input values for which the function is defined.

• The domain of a function is the set of all possible output values.

• The domain of a function is the graphical representation of the function.

• The domain of a function is the range of values that the function can produce.

How do you determine the range of a function?

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

• The range is the set of all input values.

• The range is the difference between the maximum and minimum values of the function.

• The range is determined by the function's domain.

Can a function have multiple domains? Explain.

• Yes, a function can have multiple domains.

• No, a function cannot have multiple domains.

• A function can have different domains for different inputs.

• A function's domain can change based on its output.

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

• All real numbers including zero.

• All real numbers except zero.

• Only positive real numbers.

• Only negative real numbers.

Identify the range of the function f(x) = x^2.

• [1, 2]

• (-∞, 0)

• (0, 1)

• [0, ∞)

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

• (−∞, 3)

• [3, ∞)

• [2, 3]

• (3, 5)

Explain how to find the domain of a composite function.

• The domain of a composite function f(g(x)) is the set of x values for which g(x) is defined and g(x) is in the domain of f.

• To find the domain, only consider the outer function f.

• The domain is determined solely by the inner function g.

• The domain of a composite function is always all real numbers.

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

• [-2, 2]

• [0, 2]

• [-1, 1]

• [-1, 0]

How does the graph of a function help in identifying its domain and range?

• The graph provides information about the function's slope but not its x or y values.

• The graph indicates the function's symmetry but not its domain or range.

• The graph shows only the maximum values of the function.

• The graph of a function helps identify its domain by showing the x-values where the function is defined and its range by displaying the y-values the function attains.

Provide an example of a function with a restricted domain and explain why.

• f(x) = 1/x

• f(x) = x^2

• f(x) = sin(x)

• f(x) = e^x