Understanding Domain and Range of Basic Functions

This video provides a quick review of the domain and range of nine basic functions. It begins with definitions of domain and range, explaining them as sets of possible inputs and outputs of a function, respectively. The video then examines each function, including constant, identity, absolute value, quadratic, cubic, square root, cube root, reciprocal, and reciprocal squared functions. For each, it discusses the domain and range, using graph behavior to illustrate these concepts. The video aims to help viewers understand how to determine the domain and range of these functions.

What is the domain of a function?

• The set of all possible inputs of a function

• The set of all possible outputs of a function

• The set of all negative values of a function

• The set of all positive values of a function

For the constant function f(x) = c, what is the range?

• All real numbers

• Only the constant value c

• All positive numbers

• All negative numbers

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

• Only zero

• Only negative numbers

• Only positive numbers

• All real numbers

What is the range of the absolute value function f(x) = |x|?

• Non-negative numbers

• Only zero

• Only positive numbers

• All real numbers

For the quadratic function f(x) = x^2, what is the range?

• Only positive numbers

• Non-negative numbers

• All real numbers

• Only zero

What is the domain of the cubic function f(x) = x^3?

• Only positive numbers

• All real numbers

• Only zero

• Only negative numbers

For the square root function f(x) = √x, what is the domain?

• Only zero

• All real numbers

• Non-negative numbers

• Only positive numbers

What is the domain of the cube root function f(x) = ∛x?

• Only positive numbers

• All real numbers

• Only negative numbers

• Only zero

For the reciprocal function f(x) = 1/x, what is excluded from the domain?

• All real numbers

• Zero

• Negative numbers

• Positive numbers

What is the range of the reciprocal squared function f(x) = 1/x^2?

• Only zero

• Non-negative numbers excluding zero

• Only positive numbers

• All real numbers