The reciprocal parent function is defined as \( f(x) = \frac{1}{x} \). When you replace \( f(x) = 1 \) with \( f(x) = 314 \), you are essentially introducing a constant multiplier to the function.
In the case of \( f(x) = \frac{1}{x} \) as the parent function, we analyze the effect of changing it to \( f(x) = \frac{314}{x} \):
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Reflection Across the Y-axis: There is no reflection occurring in this transformation, as both functions remain positive.
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Horizontal Compression/Stetch: The change from \( \frac{1}{x} \) to \( \frac{314}{x} \) can be seen as a vertical stretch by a factor of 314. The multiplication by a constant more than 1 stretches the graph vertically, while the horizon focuses on the x-values, where everything else remains unchanged.
Therefore, the statement that describes the effect correctly would be that there is a vertical stretch. However, the options given are focusing on horizontal transformations, which are not applicable here based on the provided changes.
From the possible answers:
- The correct transformation that should have been mentioned would be:
- The end behavior and outputs of the function will be affected (due to the constant), but with regards to the given options directly discussing horizontal compression/stretch and reflections, none perfectly capture the situation.
If required to choose an answer from the options provided, it's worth noting that there is no option that precisely reflects the vertical transformation induced by replacing 1 with 314. Thus, none of the options accurately express this situation.