Question

use the table below to determine if the inverse relation of the given function is also a function.

x	-2	-1	0	1	2
y	-16	-2	0	2	16

○ yes
○ no

Explanation:

Step1: Recall the definition of a function's inverse

A relation is a function if each input (x - value) has exactly one output (y - value). For the inverse of a function, we swap the x and y values of the original function. So first, we find the inverse relation by interchanging the x and y coordinates of the original function.

The original function has the following ordered pairs: \((-2, -16)\), \((-1, -2)\), \((0, 0)\), \((1, 2)\), \((2, 16)\)

After swapping x and y (to get the inverse relation), the ordered pairs become: \((-16, -2)\), \((-2, -1)\), \((0, 0)\), \((2, 1)\), \((16, 2)\)

Step2: Check the vertical line test for the inverse relation

To determine if the inverse relation is a function, we check if each x - value (the original y - values) has exactly one y - value (the original x - values). Let's list the x - values of the inverse relation: \(-16\), \(-2\), \(0\), \(2\), \(16\). Each of these x - values is paired with exactly one y - value. There are no repeated x - values with different y - values. So the inverse relation passes the vertical line test (each input has exactly one output).

Answer:

Yes