Chapter 8.3, Problem 44STP

To determine

To calculate: To determine which sets of ordered pairs does represents a function

Answer to Problem 44STP

All sets of ordered pairs represent a linear function.

Explanation of Solution

Given information: Given set of ordered pairs are:

  $\begin{array}{l}A.\left\{\left(2,2\right),\left(1,-1\right),\left(0,0\right),\left(-1,-1\right)\right\}\\ B.\left\{\left(4,-4\right),\left(3,-3\right)\left(2,-2\right),\left(1,-1\right)\right\}\\ C.\left\{\left(-4,-4\right),\left(0,0\right),\left(4,-4\right),\left(-8,-8\right)\right\}\\ D.\left\{\left(-3,-5\right),\left(-1,0\right),\left(0,1\right),\left(3,-5\right)\right\}\end{array}$

Formula Used:

Set of Ordered pairs is function if no two ordered pairs have the same first coordinate with different second coordinates.

Calculation:

Set of ordered pairs are given as follows:

  $\begin{array}{l}A.\left\{\left(2,2\right),\left(1,-1\right),\left(0,0\right),\left(-1,-1\right)\right\}\\ B.\left\{\left(4,-4\right),\left(3,-3\right)\left(2,-2\right),\left(1,-1\right)\right\}\\ C.\left\{\left(-4,-4\right),\left(0,0\right),\left(4,-4\right),\left(-8,-8\right)\right\}\\ D.\left\{\left(-3,-5\right),\left(-1,0\right),\left(0,1\right),\left(3,-5\right)\right\}\end{array}$

Consider $A.\left\{\left(2,2\right),\left(1,-1\right),\left(0,0\right),\left(-1,-1\right)\right\}$

Here, no two ordered pairs have the same first coordinate with different second coordinates.

Thus, set of ordered pairs represents a function

Consider $B.\left\{\left(4,-4\right),\left(3,-3\right)\left(2,-2\right),\left(1,-1\right)\right\}$

Here, no two ordered pairs have the same first coordinate with different second coordinates.

Thus, set of ordered pairs represents a function

Consider $C.\left\{\left(-4,-4\right),\left(0,0\right),\left(4,-4\right),\left(-8,-8\right)\right\}$

Here, no two ordered pairs have the same first coordinate with different second coordinates.

Thus, set of ordered pairs represents a function

Consider $D.\left\{\left(-3,-5\right),\left(-1,0\right),\left(0,1\right),\left(3,-5\right)\right\}$

Here, no two ordered pairs have the same first coordinate with different second coordinates.

Thus, set of ordered pairs represents a function

Conclusion:

Hence, all sets of ordered pairs represent a linear function.