Question

Determine if each of the equations represents a function 4x=y+8.

Short answer

The given relation 4x=y+8 is a function.

Step-by-step solution

Step 1. To find.

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

Step 2. Explanation.

A relation will be a function if

1. Every value in its domain has a unique value in its codomain.
2. For every value of x, there is a unique value of y.
3. For every value of x, there must be only one value of y.

Step 3. Calculation.

Putting x=0, 2, 3, 4 in 4x=y+8 and writing the values in the tabular form we have,

$x$	$y=4x–8$	$(x,y)$
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, the relation can be represented as:

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

From these ordered pairs we see that, for each different value of x, there is the unique value of y. It means this ordered pair satisfies the definition of a function.

Step 4. Conclusion.

From the above relation, for each x value, there is always a y value. So, 4x=y+8 is a function.