Question

An invertible function is represented by the values in the table.

X
f(x)
-3
-4.4
-2
-0.6
Which graph shows the inverse of this function?
-1
0.8
1
1.2
2
2.6
3
6.4

Answer 1

A function is invertible if and only if for every y in the range of the function, there is one and only one x in the domain such that f(x) = y. The inverse of a function is a new function that "swaps" the x and y values of the original function.

So, the inverse of a function represented by the table you provided would be a new function where the x values are -4.4, -0.6, 0.8, 1.2, 2.6 and 6.4 and the y values are -3, -2, -1, 1, 2 and 3 respectively.

The graph of the inverse function would be a reflection of the original function over the line y=x, meaning that it would be the same shape but flipped across the line y = x.