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

The transformation $$h(x) = -f(x)$$ reflects the graph of f across the x-axis.

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

The transformation $$h(x) = f(-x)$$ reflects the graph of f across the y-axis.

How does the graph of $$g(x) = f(x) + k$$ change when k is positive?

When k is positive, the graph of $$g(x) = f(x) + k$$ shifts vertically upward by k units.

How does the graph of $$g(x) = f(x) - k$$ change when k is positive?

When k is positive, the graph of $$g(x) = f(x) - k$$ shifts vertically downward by k units.

What is the effect of a horizontal shift in the function $$g(x) = f(x - h)$$ ?

The graph of $$g(x) = f(x - h)$$ shifts horizontally to the right by h units if h is positive, and to the left if h is negative.

What does a vertical stretch by a factor of 2 look like for the function $$f(x)$$ ?

A vertical stretch by a factor of 2 transforms the function to $$g(x) = 2f(x)$$ , making the graph taller.

What does a vertical compression by a factor of 1/3 look like for the function $$f(x)$$ ?

A vertical compression by a factor of 1/3 transforms the function to $$g(x) = \frac{1}{3}f(x)$$ , making the graph shorter.

What is the parent function of linear transformations?

The parent function of linear transformations is $$f(x) = x$$ .

What does the transformation $$h(x) = -\frac{1}{2}f(x) + 3$$ represent?

The transformation $$h(x) = -\frac{1}{2}f(x) + 3$$ reflects the graph of f across the x-axis, compresses it vertically by a factor of 1/2, and shifts it up by 3 units.

How can you describe the transformation from $$f(x)$$ to $$g(x) = \frac{1}{3}f(x)$$ ?

The transformation from $$f(x)$$ to $$g(x) = \frac{1}{3}f(x)$$ results in a vertical compression, making the graph of g less steep than that of f.

What is the significance of the slope in linear transformations?

The slope indicates the steepness of the graph. A larger slope means a steeper graph, while a smaller slope indicates a less steep graph.

Linear Transformations Flashcards

Student preview

15 questions

Show all answers

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 effect does adding a constant to a function have on its graph?

Back

Adding a constant to a function results in a vertical shift of the graph. If the constant is positive, the graph shifts up; if negative, it shifts down.

3.

FLASHCARD QUESTION

Front

What is the effect of multiplying a function by a constant greater than 1?

Back

Multiplying a function by a constant greater than 1 results in a vertical stretch of the graph.

4.

FLASHCARD QUESTION

Front

What is the effect of multiplying a function by a constant between 0 and 1?

Back

Multiplying a function by a constant between 0 and 1 results in a vertical compression of the graph.

5.

FLASHCARD QUESTION

Front

Back

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