
Understanding Homogeneous Functions

Interactive Video
•
Mathematics, Science
•
10th - 12th Grade
•
Hard

Amelia Wright
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the condition for a function f(x, y) to be considered homogeneous?
f(tx, ty) = alpha * f(x, y)
f(tx, ty) = t * f(x, y)
f(tx, ty) = t^2 * f(x, y)
f(tx, ty) = t^alpha * f(x, y)
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the role of alpha in a homogeneous function?
It is the coefficient of x
It is the coefficient of y
It is the degree of the function
It is the base of the power
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in determining if a function is homogeneous?
Differentiate the function
Integrate the function
Substitute tx for x and ty for y
Multiply the function by t
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What substitution is performed to check for homogeneity?
Replace x with tx and y with ty
Replace x with y
Replace y with x
Replace x with ty and y with tx
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the first example, what is the degree of the homogeneous function?
Two
One
Three
Four
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the common factor in the first example that helps determine homogeneity?
t^4
t^2
t
t^3
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the function in the second example not homogeneous?
It has a term without t
It has a term with t^3
It has a term with t^5
It has a term with t^2
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