Linear Transformation with Key Attributes
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
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 does it mean to translate a graph vertically?
Back
Translating a graph vertically means shifting the entire graph up or down along the y-axis without changing its shape.
3.
FLASHCARD QUESTION
Front
What is the effect of adding a constant to a function f(x)?
Back
Adding a constant to a function f(x) results in a vertical translation of the graph. For example, f(x) + c shifts the graph up by c units if c > 0 and down by c units if c < 0.
4.
FLASHCARD QUESTION
Front
What is a horizontal translation of a graph?
Back
A horizontal translation shifts the graph left or right along the x-axis. For example, f(x - c) shifts the graph to the right by c units, while f(x + c) shifts it to the left by c units.
5.
FLASHCARD QUESTION
Front
What is a vertical stretch of a graph?
Back
A vertical stretch occurs when the output of a function is multiplied by a factor greater than 1, making the graph taller. For example, f(x) becomes k*f(x) where k > 1.
6.
FLASHCARD QUESTION
Front
What happens to the graph of f(x) when it is reflected across the x-axis?
Back
Reflecting the graph of f(x) across the x-axis changes the sign of the output, resulting in -f(x). This flips the graph upside down.
7.
FLASHCARD QUESTION
Front
How does a horizontal compression affect a graph?
Back
A horizontal compression occurs when the input of a function is multiplied by a factor greater than 1, making the graph narrower. For example, f(k*x) where k > 1 compresses the graph horizontally.
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