To transform the function \( f(x) = x + 2 \) according to the specified transformation rule "re-azis," we need to break down what that might entail. The term "re-azis" appears to be a typo or a miscommunication, as it's unclear what specifically it refers to in the context of function transformations.
However, I'll provide you with a basic understanding of the common transformations of functions, which can include shifts (translations), stretches, compressions, and reflections.
Let's denote \( g(x) \) as a transformation of \( f(x) \). Here are some common transformations and how they would be represented:
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Vertical Shift:
- Upward: \( g(x) = f(x) + k \) (where \( k > 0 \))
- Downward: \( g(x) = f(x) - k \) (where \( k > 0 \))
-
Horizontal Shift:
- Right: \( g(x) = f(x - h) \) (where \( h > 0 \))
- Left: \( g(x) = f(x + h) \) (where \( h > 0 \))
-
Vertical Stretch/Compression:
- Stretch: \( g(x) = a \cdot f(x) \) (where \( a > 1 \))
- Compression: \( g(x) = a \cdot f(x) \) (where \( 0 < a < 1 \))
-
Horizontal Stretch/Compression:
- Stretch: \( g(x) = f(bx) \) (where \( 0 < b < 1 \))
- Compression: \( g(x) = f(bx) \) (where \( b > 1 \))
-
Reflection:
- About the x-axis: \( g(x) = -f(x) \)
- About the y-axis: \( g(x) = f(-x) \)
If you meant to apply a specific type of transformation (such as a vertical shift or horizontal shift), please clarify the transformation you would like to apply.
To summarize, the general form for a transformation \( g(x) \) that shifts or modifies \( f(x) \) can be structured like this:
\[ g(x) = a \cdot f(b(x - h)) + k \]
Where:
- \( a \) = vertical stretch/compression/reflection
- \( b \) = horizontal stretch/compression/reflection
- \( h \) = horizontal shift
- \( k \) = vertical shift
Given that "re-azis" is unclear, please provide more details so that I can assist you more accurately!
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