Chapter 8, Problem 1MCP

To determine

Whether the given relation is a function or not, and domain and range of the relation.

  $\left\{\left(2,6\right),\left(1,4\right),\left(2,-6\right)\right\}$

Answer to Problem 1MCP

Solution:

The given relation is not a function.

  $\text{Domain =}\left\{2,1\right\}$

  $\text{Range =}\left\{6,4,-6\right\}$

Explanation of Solution

Given:

$\left\{\left(2,6\right),\left(1,4\right),\left(2,-6\right)\right\}$

Concept used:

For a relation to be a function each input should have one and only one output.

Domain is the set of values of $x$ in the ordered pair $\left(x, y\right)$ .

Range is the set of values of $y$ in the ordered pair $\left(x, y\right)$ .

Calculation:

Since at $x=2$ , we get two different values of $\text{y}$ i.e. $y=-6$ , so this relation is not a function.

  $\text{Domain =}\left\{2,1\right\}$

  $\text{Range =}\left\{6,4,-6\right\}$

Conclusion:

The given relation is not a function, and its domain is $\left\{2,1\right\}$ , and the range is $\left\{6,4,-6\right\}$ .

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