What is the difference between a vertical stretch and a vertical compression?

A vertical stretch increases the distance of points from the x-axis, while a vertical compression decreases it.

What is the general form of a linear transformation?

The general form is $$g(x) = af(x) + b$$ , where a is a scaling factor and b is a vertical shift.

How do you identify a vertical shift in a function?

A vertical shift can be identified by the constant added or subtracted from the function, e.g., $$g(x) = f(x) + c$$ .

What is the impact of a negative scaling factor in a transformation?

A negative scaling factor reflects the graph across the x-axis.

What is the significance of the coefficient in front of f(x) in transformations?

The coefficient determines the vertical stretch or compression of the graph.

How can you determine the transformation from a graph?

By comparing the original function's graph to the transformed graph, you can identify shifts, stretches, or reflections.

Linear Transformations Flashcards

Student preview

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 the transformation $g(x) = f(x) + 3$ represent?

Back

This transformation shifts the graph of the function f(x) upward by 3 units.

3.

FLASHCARD QUESTION

Front

What does the transformation $g(x) = f(x) - 3$ represent?

Back

This transformation shifts the graph of the function f(x) downward by 3 units.

4.

FLASHCARD QUESTION

Front

What does the transformation $g(x) = 3f(x)$ represent?

Back

This transformation stretches the graph of the function f(x) vertically by a factor of 3.

5.

FLASHCARD QUESTION

Front

What does the transformation $g(x) = \frac{1}{4}f(x)$ represent?

Back

This transformation compresses the graph of the function f(x) vertically by a factor of 4.

6.

FLASHCARD QUESTION

Front

What does dilating a graph by a factor of -3 mean?

Back

It means to stretch the graph away from the origin by a factor of 3 and reflect it across the x-axis.

7.

FLASHCARD QUESTION

Front

What is the effect of the transformation $g(x) = f(x) + 6$ ?

Back

This transformation shifts the graph of the function f(x) upward by 6 units.

8.

FLASHCARD QUESTION

Front

What is the effect of the transformation $g(x) = f(x) - 6$ ?

Back

This transformation shifts the graph of the function f(x) downward by 6 units.

9.

FLASHCARD QUESTION

Front

What is the effect of the transformation $g(x) = 6f(x)$ ?

Back

This transformation stretches the graph of the function f(x) vertically by a factor of 6.

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