Describe the transformation represented by $$g(x + 4) - 6$$ .

The graph of the function is shifted 4 units left and 6 units down.

What is the effect of a negative sign in front of a function, such as $$-f(x)$$ ?

A negative sign reflects the graph of the function across the x-axis.

What is the effect of a transformation like $$g(x) = f(x - 5) + 2$$ ?

This transformation shifts the graph of f(x) 5 units to the right and 2 units up.

What does the notation $$g(x) = f(x + c)$$ indicate?

This indicates a horizontal shift of the graph of f(x) to the left by c units.

What is the general form of a function transformation?

The general form is $$g(x) = a \times f(b(x - h)) + k$$ , where a affects vertical stretch/compression, b affects horizontal stretch/compression, h shifts horizontally, and k shifts vertically.

How does changing the value of 'a' in $$g(x) = a \times f(x)$$ affect the graph?

Changing 'a' affects the vertical stretch or compression of the graph. If |a| > 1, the graph stretches; if 0

What does the term 'reflection' mean in function transformations?

Reflection means flipping the graph over a specific axis. For example, reflecting over the x-axis is done by multiplying the function by -1.

Transformations of Functions Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is a vertical shift in function transformations?

Back

2.

FLASHCARD QUESTION

Front

Back

The graph of the function is shifted 3 units up.

3.

FLASHCARD QUESTION

Front

What is a horizontal shift in function transformations?

Back

4.

FLASHCARD QUESTION

Front

Back

The graph of the function is shifted 5 units right and 2 units up.

5.

FLASHCARD QUESTION

Front

What does a vertical stretch by a factor of k do to a function?

Back

6.

FLASHCARD QUESTION

Front

Back

The graph of the function is vertically stretched by a factor of 4, making it narrower.

7.

FLASHCARD QUESTION

Front

What does a vertical compression by a factor of k do to a function?

Back

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