Question

For each set of ordered pairs, determine if it represents a function and if so, is the function one-to-one.

$$\begin{gathered} ⓐ(-3,-6),(-2,-4),(-1,-2),(0,0),(1,2),(2,4),(3,6) \\ ⓑ(-4,8),(-2,4),(-1,2),(0,0),(1,2),(2,4),(4,8) \end{gathered}$$

Short answer

Part (a) Each x-value is matched with only one y-value. So this relation is a function.

Since each y-value is paired with only one x-value, this function is one-to-one.

Part (b) Each x-value is matched with only one y-value. So this relation is a function. But each y-value is not paired with only one x-value. So this function is not one-to one.

Step-by-step solution

Step 1. Given information

The given ordered pairs are

$$\begin{gathered} ⓐ(-3,-6),(-2,-4),(-1,-2),(0,0),(1,2),(2,4),(3,6) \\ ⓑ(-4,8),(-2,4),(-1,2),(0,0),(1,2),(2,4),(4,8) \end{gathered}$$

Part (a) Step 2. Calculation

$ⓐ(-3,-6),(-2,-4),(-1,-2),(0,0),(1,2),(2,4),(3,6)$

Each x-value is matched with only one y-value. So this relation is a function. Since each y-value is paired with only one x-value, this function is one-to-one.

Part (b)Step 3. 

$ⓑ(-4,8),(-2,4),(-1,2),(0,0),(1,2),(2,4),(4,8)$

Each x-value is matched with only one y-value. So this relation is a function. But each y-value is not paired with only one x-value,$\left[(-4,8),(4,8)\right]\left[(-2,4),(2,4)\right],\left[(-1,2),(1,2),\right]$ , for example. So this function is not one-to one.