To determine which function, \( r \) or \( s \), is the inverse of function \( q \), we need to analyze the properties of these functions and their graphs.
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Function \( q \): The left half of a parabola opening upwards with vertex \( (0, -5) \). This suggests that it is a quadratic function which may resemble a half of \( y = a(x - 0)^2 - 5 \), where it only exists for \( x \leq 0 \).
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Function \( r \): A curve starting at \( (-5, 0) \) and curving downwards to the right. This would suggest that \( r \) is possibly a decreasing function.
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Function \( s \): The left half of a downward facing parabola with vertex \( (0, 1.5) \). This suggests that it is a quadratic function that opens downwards and exists for \( x \leq 0 \).
For one function to be the inverse of another, their graphs must be symmetrical about the line \( y = x \).
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The left half of a parabola opening upwards (function \( q \)) does indeed have an inverse that will be a curve that reflects over the line \( y = x \).
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Function \( r \), which starts at \( (-5, 0) \) and curves down, likely represents the inverse of the left half of a parabola since it will reflect the behavior of \( q \) in such a way that for a given \( y \) value from \( q \), a corresponding \( x \) value can be found in \( r \).
Therefore, the function \( r \) is symmetrical about the line \( y = x \) with respect to function \( q \).
Based on the analysis, the correct response is:
- the function r because the graphs of q and r are symmetrical about the line y = x.
1 answer