Chapter 7.3, Problem 52HP

To determine

To Explain:

Why $y=\pm \sqrt{x}$ is not a function.

Explanation of Solution

Concept Used:

A function is :

A relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

So, for 1 value of x , there should be only 1 value of y .

Calculation:

  $\begin{array}{l}Given\text{ function:}\\ y=\pm \sqrt{x}\\ Let\\ x=1\\ \Rightarrow y=\pm 1\\ \text{Since , for one x-value , the function has two y-values}\text{.}\\ \text{To be a function , for every x-value there must be exactly}\\ \text{one y-value}\text{.}\\ \text{Or the graph of the equation should pass the vertical line test,}\\ that\text{ is , the vertical line should intersect the graph at exactly }\\ \text{one point for it to be a function}\text{.}\\ \text{But here , the equation has two y-values ; one is positive and}\\ \text{other one is negative for each x-value}\text{.}\\ \text{Also, the graph of the equation does not pass the vertical line test}\text{.}\\ \text{So, the given equation is not a function}\text{.}\end{array}$