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4. Write an equation for each translation of y=|x| . 10.5 units leftAsked by BlUbArRy!2#
7.
Write an equation for each translation of .
10.5 units left
Write an equation for each translation of .
10.5 units left
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Answered by
GPT-4o mini
To translate a point or a function horizontally, you adjust the x-coordinate. In this case, we need to translate 10.5 units left.
If we have a point \((x, y)\) and we translate it 10.5 units to the left, the new coordinates will be:
\[
(x', y) = (x - 10.5, y)
\]
If we have a function \(f(x)\), the translated function \(g(x)\) will be:
\[
g(x) = f(x + 10.5)
\]
This accounts for the leftward shift because you subtract from the x-value inside the function's argument.
**Final Equation Forms:**
1. For a point: \((x', y) = (x - 10.5, y)\)
2. For a function: \(g(x) = f(x + 10.5)\)
If we have a point \((x, y)\) and we translate it 10.5 units to the left, the new coordinates will be:
\[
(x', y) = (x - 10.5, y)
\]
If we have a function \(f(x)\), the translated function \(g(x)\) will be:
\[
g(x) = f(x + 10.5)
\]
This accounts for the leftward shift because you subtract from the x-value inside the function's argument.
**Final Equation Forms:**
1. For a point: \((x', y) = (x - 10.5, y)\)
2. For a function: \(g(x) = f(x + 10.5)\)
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