Chapter 4.2, Problem 4LC

To determine

whether the each set of ordered pairs in exercise $1$ represents a function.

Explanation of Solution

Given information:

The odred pairs in exercise 1 are:

  $\left\{\left(0,0\right),\left(1,1\right),\left(2,2\right),\left(3,3\right),\left(4,4\right)\right\}$

  $\left\{\left(0,8\right),\left(1,6\right),\left(2,4\right),\left(3,2\right),\left(4,0\right)\right\}$

  $\left\{\left(3,0\right),\left(3,1\right),\left(3,2\right),\left(3,3\right),\left(3,4\right)\right\}$

Calculation:

The necessary condition for a function is that each input value is coupled with exactly one output value.

From the ordered pairs in exercise $1$ in part $a$ , the each input value has the exactly one output value, therefore the ordered pairs in part $a$ represents a function.

In part $b$ , each input value has exactly one output value, therefore the ordered pairs represents a function.

In part $c$ , only one input has more than one output value , therefore the ordered pairs do not represents a function.