How come

x: -1,0,1,2,3,4
y:-2,1,2,1,-2,6

does not have an inverse? I don't see why you just can't flip the x and y values (for example X:-2, y:-1) and have that be the inverse. Could you explain?

There is not a one-to-one mapping, look at y=-2

Thanks

To determine whether a function has an inverse, we need to check if the function satisfies the horizontal line test. The horizontal line test states that every horizontal line should intersect the graph of the function at most once.

In this case, let's consider the points (x, y):

x: -1, 0, 1, 2, 3, 4
y: -2, 1, 2, 1, -2, 6

If we plot these points on a graph, we can see that the graph does not pass the horizontal line test. For example, the points (-1, -2) and (2, 1) have the same y-coordinate but different x-coordinates.

To further understand why this graph does not have an inverse, we can review the definition. The inverse of a function swaps the x and y values. However, for every x value in the given set, there are multiple corresponding y values. For instance, x = 2 has two corresponding y values: 1 and 6.

Because there are multiple y values for some x values, this function does not satisfy the necessary condition for an inverse function. To have an inverse, each x value must have a unique y value and vice versa.

In summary, the given set of points does not have an inverse because it does not satisfy the horizontal line test and multiple y values correspond to certain x values.