Question

Which graphed function has an inverse that is not a function?


Responses

The graph of a straight line that slants down from left to right. The line passes through the points 0, 2 and 2, 0.
Pick the answer below.

The graph of a line that starts at negative 1, 2 and curves down to the right.
Pick the answer below.

The graph of a horizontal line that passes through the point 0, 2.
Pick the answer below.

Answer 1

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:

1. **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.

2. **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.

3. **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).**