an example of an equation that is not a function?

Question

need help understanding. Can someone show me an equation that is not a function? Thank You.

Answer 1

y=4 is a function

x=4 however, is not. A function is a relation of which for every input there is only one output. x=4 does not satisfy this.

You can tell if something is a function through a "vertical line test". Basically, after you graph the equation, if you can draw a vertical line anywhere on the graph and it intersects the graph more than once, then it is not a function. x=4 is not a function, because x=4 is just basically a vertical line at x=4. Doing a vertical line test at x=4 shows that the line will intersect an infinite amount of times, and thus it is not a function. Another equation which is not a function is a circle

x^2+y^2= r^2

Answer 2

A function has only one output y for each input x. So, as an example, the equation y^2 = x describes a sideways parabola with vertex at the origin; it is not a function, however, because the y values of both 2 and -2, for example, are described by the single value x=4.

Other examples are x^2 + y^2 = 1 (a circle with radius 1, centered at the origin), y^4 = x, y=0, etc.

Answer 3

Piecewise function are applications with 2 or extra different regulations, reckoning on what x is. For this, you will see that that if 3x - 4 > 0 (it would want to't = 0 because that is on bottom of a fragment), absolutely the fee bars may don't have any result so that you may want to bypass over them. And if 3x - 4 > 0 , 3x > 4 so x > 4/3. yet when 3x - 4 < 0, absolutely the fee converts it to its opposite, that is 4 - 3x. So your piecewise function is g(x) = (2x+5) / (3x-4), x > 4/3       = (2x+5) / (4 - 3x), x < 4/3 and typically you type of positioned a huge curly brace { enclosing the left ends of the formulation

Answer 4

y = 4 is an equation that is not a function


Doug

Answer 5

yes all equations because equations cannot be functions