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

1 Answer
Jun 1, 2018

See explanation below


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

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

#y=+-sqrt(4x)# 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]}