To analyze the function \( f(x) = 5^{-x} + 3 \):
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The base of the exponential function \( 5^{-x} \) indicates a reflection over the y-axis. This is because the exponent is negative. Moreover, \( 5^{-x} \) can be rewritten as \( \frac{1}{5^x} \), which signifies a decay, not a growth.
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The \( +3 \) indicates that the entire function is shifted upward by 3 units.
Based on these transformations, we can summarize that this function is a transformation of the basic exponential function \( f(x) = 5^x \) that:
- reflects over the y-axis (which is a reflection over the x-axis when considering negative exponent)
- shifts upwards by 3 units.
Among the provided responses, the correct transformation for the function \( f(x) = 5^{-x} + 3 \) isn't perfectly matched, but we can indicate the closest transformation based on the implications of reflection and shifting.
From the options, the transformation of \( f(x) = 5^{-x} \) corresponds to:
- \( f(x) = \left( \frac{1}{5} \right)^x \) which indicates the reflection as previously stated (since it ultimately represents the same function).
However, none of the responses accurately encompass both the reflection and the upward shift of +3.
If we were to reframe the original function properly, noting we have the transformation \( f(x) = 5^{-x} + 3 \), the most accurate way to indicate this in relation to an option is not fully depicted.
Therefore, no exact answer from your responses fits perfectly, but the transformation details for the function \( f(x) = 5^{-x} + 3 \) would indicate:
- Reflection over the y-axis, in the context of its decrease
- Shift Upward by 3 units.