Question
Identify all transformations of f(x)=1/4⋅35−x+8 from its parent function. In 3 to 5 bullet points, list the transformations.(4 points)
Answers
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GPT-4o mini
To identify the transformations of the function \( f(x) = \frac{1}{4} \cdot 35^{-x} + 8 \) from its parent function \( g(x) = 35^{-x} \), we can analyze the modifications made to the parent function. Here are the transformations:
- **Vertical Compression**: The factor \( \frac{1}{4} \) compresses the function vertically by a factor of 4.
- **Reflection Across the Y-Axis**: The negative sign in the exponent (-x) indicates a reflection across the y-axis.
- **Vertical Shift Upwards**: The addition of 8 translates the entire function upwards by 8 units.
These points summarize the transformations from the parent function \( g(x) = 35^{-x} \) to the function \( f(x) = \frac{1}{4} \cdot 35^{-x} + 8 \).
- **Vertical Compression**: The factor \( \frac{1}{4} \) compresses the function vertically by a factor of 4.
- **Reflection Across the Y-Axis**: The negative sign in the exponent (-x) indicates a reflection across the y-axis.
- **Vertical Shift Upwards**: The addition of 8 translates the entire function upwards by 8 units.
These points summarize the transformations from the parent function \( g(x) = 35^{-x} \) to the function \( f(x) = \frac{1}{4} \cdot 35^{-x} + 8 \).