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Questions and Answers
What is the result of reflecting a function across the x-axis?
What is the result of reflecting a function across the x-axis?
- f(-x)
- -f(x) (correct)
- f(x-a)
- f(x) + a
What is the result of reflecting a function across the y-axis?
What is the result of reflecting a function across the y-axis?
- f(x+a)
- f(x) - a
- -f(x)
- f(-x) (correct)
What does the expression f(x+a) represent?
What does the expression f(x+a) represent?
- Vertical shift up
- Reflection across the x-axis
- Horizontal shift right
- Horizontal shift left (correct)
What does the expression f(x-a) represent?
What does the expression f(x-a) represent?
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What does f(x) + a represent?
What does f(x) + a represent?
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What does f(x) - a represent?
What does f(x) - a represent?
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A vertical stretch is indicated by the condition a > 1.
A vertical stretch is indicated by the condition a > 1.
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Study Notes
Reflection Rules
- Reflection across the x-axis is represented by the equation -f(x), which flips the graph over the x-axis.
- Reflection across the y-axis is denoted by f(-x), which flips the graph over the y-axis.
Shift Rules
- A horizontal shift to the left is expressed as f(x+a), moving the graph left by 'a' units.
- A horizontal shift to the right is shown as f(x-a), moving the graph right by 'a' units.
- A vertical shift upwards is characterized by f(x) + a, lifting the graph up by 'a' units.
- A vertical shift downwards is represented by f(x) - a, lowering the graph down by 'a' units.
Stretch Rules
- A vertical stretch occurs when the function is multiplied by a factor 'a' where a > 1, making the graph steeper.
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