Q3A. - Algebra 1

Question

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

Step-by-Step Solution

Answer

The given relation is not a function because, for two same input values, there is always a different output value.

Step 1. To find.

The relation $4x=8$ i.e. $0y+x=\frac{8}{4}=2$ is a function.

Step 2. From question.

The relation is $4x=8$.

Step 3. 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 4. Calculation.

We can write the given relation as, so it can be written as a set of ordered pairs as:

$R=\{\left(2,0\right),\left(2,1\right),\left(2,3\right)\dots .\}$

We see that, for any two same x values, there is a different y value in ordered pairs.

That means for a value of x, there are more than values of y.

Step 5. Conclusion.

From the above relation, for the same x values, there is always a different y value. So, this relation is not a function.