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Questions and Answers
What is a vertical stretch?
What is a vertical stretch?
- Outside parenthesis F(x)-->A times F(x) (correct)
- A horizontal shift
- A reflection over the y-axis
- Inside parenthesis F(x)-->f(1/b x)
What does the vertical compression do to the function F(x)?
What does the vertical compression do to the function F(x)?
F(x)-->A times F(x)
Which transformation is represented by F(x)-->f(1/b x)?
Which transformation is represented by F(x)-->f(1/b x)?
- Vertical Stretch
- Reflection over the x-axis
- Horizontal Stretch (correct)
- Vertical Shift
What type of transformation is indicated by F(x)-->-F(x)?
What type of transformation is indicated by F(x)-->-F(x)?
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What does a horizontal shift do in terms of function transformation?
What does a horizontal shift do in terms of function transformation?
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What is the representation of a vertical shift in a transformation function?
What is the representation of a vertical shift in a transformation function?
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Study Notes
Vertical Transformations
- Vertical stretch occurs outside the parenthesis, represented as F(x) = A * F(x).
- Example: A vertical stretch of 2 for the function translates to 2(x) or 2(x + 4).
- Vertical compression also occurs outside the parenthesis, represented similarly as F(x) = A * F(x).
- Example: A vertical compression by 1/2 results in 1/2(x) or 1/2(x + 4).
Horizontal Transformations
- Horizontal stretch is defined inside the parenthesis, taking the form F(x) = f(1/b * x) and affects the input.
- Example: A horizontal stretch of 1/2 is reflected in the function as (1/2)x or (1/1/2 * x + 4) when expanded.
- Horizontal compression also occurs inside the parenthesis, affecting the function input.
- Example: A horizontal compression by 2 results in (2x) or (2x + 4).
Reflections
- Reflection over the y-axis is represented by F(x) = f(-x), flipping the graph horizontally.
- Reflection over the x-axis is represented by F(x) = -F(x), flipping the graph vertically.
Shifts
- Horizontal shift is defined by F(x) = f(x - h), moving the graph left or right based on the value of h.
- Vertical shift is represented as F(x) = f(x) + k, moving the graph up or down depending on the value of k.
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