table 1:

x: -2,-1, 0, 1, 2
y: 2, 1, 0, -2, -1
is this a inver

1 answer

To determine if the given set of points in Table 1 represents a function that is invertible, we need to check if the relationship between \( x \) and \( y \) is one-to-one. A function is one-to-one (and therefore invertible) if each output \( y \) corresponds to exactly one input \( x \).

Given the pairs:

  • \((-2, 2)\)
  • \((-1, 1)\)
  • \((0, 0)\)
  • \((1, -2)\)
  • \((2, -1)\)

We can observe the outputs (or \( y \) values):

  • For \( y = 2 \), \( x = -2 \)
  • For \( y = 1 \), \( x = -1 \)
  • For \( y = 0 \), \( x = 0 \)
  • For \( y = -2 \), \( x = 1 \)
  • For \( y = -1 \), \( x = 2 \)

Each output \( y \) value is unique and corresponds to a single input \( x \) value. Therefore, the function defined by these points is one-to-one.

Since the function is one-to-one, it has an inverse. Thus, based on the information provided in Table 1, we can conclude that the relationship between \( x \) and \( y \) is invertible.