# How do you decide whether the relation y^2 =4x defines a function?

Jun 1, 2018

See explanation below

#### Explanation:

A function is an application such that, for EACH $x$ the image is UNIQUE.

In our expresion ${y}^{2} = 4 x$ if we apply square roots in both sides we have

$y = \pm \sqrt{4 x}$ in this expresion, for each $x$ we have two values for $y$ (negative and positive), So the expresion doesn`t define a function

A similar approach working with graphs. If we draw a vertical line, (parallel to y axis) this line cut or intercept graph in only one point in plane. If vertical line intercept in two or more points, the graph doesn't define a function.

Hope this helps

Note: the relation above define a parabola (plane curve, not function) like this
graph{y^2=4x [-10, 10, -5, 5]}