Chapter 1.7, Problem 3BGP

To determine

To find:

If the given relation $4x=y+8$ is a function.

Answer to Problem 3BGP

Yes, given relation is a function because for two different input values, there is always a differentunique output value.And given one is a linear function actually as its degree is one.

Explanation of Solution

Given information:

Given a relation, $4x=y+8$ .

Concept used:

A relation is a function,

• If for each value in its domain; there is always a unique value in its co domain.
• If for each different first value of its ordered pair, there is always a second unique value, then such relation is a function always.
• Or, no two same first values, should have two different second values in ordered pairs of set of relation.

Calculation:

In tabular form, given relation can be written in its ordered pair form as:

x	$y=4x-8$	$(x,y)$
0	$y=4\left(0\right)-8=-8$	$(0,-8)$
2	$y=4\left(2\right)-8=0$	$(2,0)$
3	$y=4\left(3\right)-8=4$	$(3,4)$
4	$y=4\left(4\right)-8=8$	(4,8))

Or, given relation as a set of ordered pairs can be represented as:

  $R=\{\left(0,-8\right),\left(2,0\right),\left(3,4\right)\dots .\}$

So, for each different input value of x , there is always a unique output value of variable y . That satisfies the definition of a function.

Conclusion:

So, inabove relation, for each different first value, there is always a unique second value in its given ordered pairs. So, it is surely a function, based on definition of the function.