Question

hi I have to determine if y^2=x-3 is a function using the vertical lime test. however I don't understand how to graph it.

Answer 1

The Vertical Line Test of a Function

When the graph of a function is given, we can use the vertical line test to find if it's a function or not.

Recall a function must satisfy the condition that for any value of x there should be only one value of y.

If we draw a vertical line and the graph of the function is intercepted (or touched) by the line more than once, then it's not the graph of a function.

We are given the equation:

`y^2=x-3`

Solving for x:

`x=y^2+3`

Let's give y the values: y={-2, -1, 0, 1, 2} and calculate x.

For y=2 and y=-2 we get the same value for x because any number squared is positive:

`\begin{gathered} x=2^2+3 \\ x=7 \end{gathered}`

Thus we have the points (7,2) and (7,-2)

For y=1 and y=-1 we get the points (4,1) and (4,-1)

For y=0 we have the point (3,0).

The graph is shown below:

As seen, it's possible to draw a vertical line that intercepts the graph twice. Thus the graph does not correspond to a function