To determine which graphed function has an inverse that is not a function, we can apply the horizontal line test. A function's inverse will not be a function if there exists a horizontal line that intersects the graph of the function at more than one point.
Let's analyze the provided options:
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The graph of a straight line that slants down from left to right, passing through the points (0, 2) and (2, 0):
- This represents a linear function with a non-zero slope. It will pass the horizontal line test, meaning its inverse will also be a function.
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The graph of a line that starts at (-1, 2) and curves down to the right:
- Assuming this is a nonlinear function (like a quadratic or another curve), we need more information about its shape. If the curve has a maximum point and then goes back down, a horizontal line could intersect it at two points, indicating that the inverse would not be a function.
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The graph of a horizontal line that passes through the point (0, 2):
- A horizontal line is constant and will not pass the vertical line test, meaning it fails to be a function. Its inverse will therefore not be a function.
From this analysis, the second option (the curved line) and the third option (horizontal line) have the potential not to produce a function as their inverse. However, since the horizontal line definitely fails the vertical line test, we can conclude:
The graph of a horizontal line that passes through the point (0, 2).
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