Question

Determine whether the relation y^2 - 4x = 3 represents y as a function of x ​

Answer 1

The relation
`y^(2) - 4x = 3` does not represent y as a function of x.

Explanation:

Consider the relation

`y^(2) - 4x = 3`

`y=\pm √(4x+3)`

Thus, the equation
`y=\pm √(4x+3)` does not represent function because there is at least one x-value with two or more values.

For example, if you look at the attached graph,

at x = 0, y = 1.73

at x = 0 , y = -1.73

It means the same input is generating two outputs; also if we draw a vertical line on the graph, the vertical line would intersect the graph more than once.

Please check the red vertical line on the graph would intersect the graph more than once.

Therefore, the relation
`y^(2) - 4x = 3` does not represent y as a function of x.