A vector valued function is a mathematical function that maps a set of inputs to a set of outputs, where both the inputs and outputs are vectors. It can be represented as f(x) =
To graph a vector valued function, you can plot points on a coordinate plane using the input vector as the x-axis and the output vector as the y-axis. The resulting plot will show the direction and magnitude of the function at each input point.
The domain of a vector valued function is the set of all possible input vectors, while the range is the set of all possible output vectors. In other words, the domain is the set of all values that can be plugged into the function, and the range is the set of all values that the function can produce.
The derivative of a vector valued function is a vector of derivatives, where each component is the derivative of the corresponding component of the original function. To find the derivative, you can use the rules of vector calculus, such as the product rule or chain rule.
Vector valued functions have many practical applications, including in physics, engineering, economics, and computer graphics. For example, they can be used to model the motion of objects in space, analyze the forces acting on a system, or create 3D animations and simulations.