
Understanding Domains of Vector-Valued Functions

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned

Ethan Morris
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the domain of a vector-valued function R(t) if its components are X(t), Y(t), and Z(t)?
The domain of X(t) only
The domain of Y(t) only
The intersection of the domains of X(t), Y(t), and Z(t)
The union of the domains of X(t), Y(t), and Z(t)
Tags
CCSS.HSF-BF.A.1B
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the intersection of domains in determining the domain of a vector-valued function?
It determines the range of the function
It identifies the common domain where all components are defined
It is not significant
It only affects the domain of X(t)
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In Example 1, what is the domain of the vector-valued function R(t) with components X(t) = 2sin(t), Y(t) = cos(2t), and Z(t) = ln(t+2)?
t > -2
t < 0
t < -2
t > 0
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In Example 1, which component function restricts the domain of the vector-valued function R(t)?
Y(t) = cos(2t)
X(t) = 2sin(t)
None of the components
Z(t) = ln(t+2)
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
For Example 2, which value of t is not included in the domain of the vector-valued function R(t) with components X(t) = 5t^2, Y(t) = 1/t, and Z(t) = 1/(t+3)?
t = 2
t = 3
t = 1
t = 0
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In Example 2, what is the domain of the vector-valued function R(t) using interval notation?
(-∞, 0) ∪ (0, 3) ∪ (3, ∞)
(0, ∞)
(-∞, 3)
(0, 3)
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In Example 3, what is the domain of the vector-valued function R(t) when all component functions have domains of all real numbers?
All real numbers
t > 1
t < 0
t > 0
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