Linear Transformations Review

Flashcard
•
Mathematics
•
10th - 11th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a linear transformation?
Back
A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.
2.
FLASHCARD QUESTION
Front
What is the parent function of linear functions?
Back
The parent function of linear functions is f(x) = x.
3.
FLASHCARD QUESTION
Front
How does the function g(x) = f(x) + c transform the graph of f(x)?
Back
The graph of f(x) is shifted vertically by c units. If c is positive, it shifts up; if c is negative, it shifts down.
4.
FLASHCARD QUESTION
Front
How does the function g(x) = f(x - c) transform the graph of f(x)?
Back
The graph of f(x) is shifted horizontally by c units. If c is positive, it shifts right; if c is negative, it shifts left.
5.
FLASHCARD QUESTION
Front
What effect does multiplying a function by a constant have?
Back
Multiplying a function by a constant a (g(x) = a * f(x)) results in a vertical stretch if |a| > 1, and a vertical compression if 0 < |a| < 1.
6.
FLASHCARD QUESTION
Front
What is the transformation represented by g(x) = f(x) - 6?
Back
The graph of f(x) is shifted down 6 units.
7.
FLASHCARD QUESTION
Front
What is the transformation represented by g(x) = f(x + 3)?
Back
The graph of f(x) is shifted left 3 units.
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