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y=-2(4)^x+1 +1 describe transformation

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Answer to a math question y=-2(4)^x+1 +1 describe transformation

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Adonis
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106 Answers
Solution:
1. Given function:
* y = -2(4)^{x+1} + 1

2. Base function:
* y = 4^x

3. Identify transformations step-by-step:
- **Translation horizontally**: The function has (x+1) as the exponent instead of x. This indicates a horizontal shift to the left by 1 unit.
- **Vertical stretch and reflection**: The coefficient before 4 is -2.
- **Vertical stretch**: The factor 2 indicates that the function is stretched vertically by a factor of 2.
- **Reflection**: The negative sign indicates a reflection across the x-axis.
- **Vertical translation**: The +1 outside the function indicates a vertical shift upwards by 1 unit.

4. Describe the complete transformation:
- The function y = 4^x undergoes the following transformations: a horizontal shift to the left by 1 unit, a vertical stretch by a factor of 2, reflection across the x-axis, and finally a vertical shift upwards by 1 unit.

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