EDGE Math 8

Functions

Note that there are equations that cannot be classified as functions. If one value of x can be paired with more than one value of y, the equation does not define y as a function of x.

Example

Prove that the equation $y^{2} = x$ does not define y as a function of x.

Solution

Solve for y in terms of x in the given equation.

$y^{2}$	$=$	$x$
$y$	$=$	$\pm \sqrt{x}$

The symbol $\pm$ in the equation shows that for every x, there are two values of y, one taking the positive sign and the other one the negative sign. For example, if $x = 4,$ then $y = \pm \sqrt{4} = \pm 2.$ Hence, y can be +2 or –2. Notice that one value of x gives two values of y. Thus, the equation does not define y as a function of x.