Understanding the Domain of Vector-Valued Functions

This video tutorial explains how to determine the domain of vector-valued functions by finding the intersection of the domains of their component functions. It provides examples with two and three components, using natural logarithms, square roots, and cosine functions. The video also demonstrates how to express domains using interval notation and graphically represent them to find intersections.

What is the domain of a vector-valued function?

• The domain of the last component function

• The domain of the first component function

• The intersection of the domains of its component functions

• The union of the domains of its component functions

When a vector-valued function has only two components, which domains do we consider?

• Neither x nor y components

• Only the x component

• Only the y component

• Both x and y components

What is the domain of the function natural log(t + 1)?

• t >= -1

• t < -1

• t = -1

• t > -1

How is the domain of the square root of (4 - t^2) expressed in interval notation?

• [2, ∞)

• (-2, 2)

• [-2, 2]

• (-∞, 2]

What does the intersection of two domains represent in a vector-valued function?

• The common values in both domains

• The union of all possible values

• The values exclusive to one domain

• The sum of both domains

What is the domain of the function natural log(t)?

• t >= 0

• t > 0

• t < 0

• t = 0

How is the domain of the square root of (t + 2) expressed in interval notation?

• [2, ∞)

• (-2, ∞)

• [-2, ∞)

• (-∞, -2]

What is the domain of the cosine function?

• Only integers

• Only negative numbers

• Only positive numbers

• All real numbers

In the example with three components, what is the final domain of the vector-valued function?

• t >= 0

• t > 0

• t < 0

• t = 0

What is the interval notation for the domain of a vector-valued function with t > 0?

• (-∞, 0)

• [0, ∞)

• (-∞, ∞)

• (0, ∞)