I cannot seem to get y by itself and make it work in a graph. I need to determine whether the following is a function: y^2=3x^2-4x-8. Can someone help explain how to get y by itself so I am able to graph it.Thank you!

A function assigns to every x-value in its domain unique y-value.

The equation

y²=3x²-4x-8

is

**not**a function. To see this, we should first determine for which values of x the equation is even defined. Sincey²≥0, we must have 3x²-4x-8≥0.

You can solve this inequality with the quadratic formula and will find that the allowed values for x are

(-∞,-(2/3)√7+(2/3)] ∪ [(2/3)√7+(2/3),∞)

Let's take one of those allowed x-values, let's say x=10, and see what happens:

y²=3x²-4x-8=3(10)²-4(10)-8=252

Now y can be +√252 or -√252, so there is no unique y-value for x=10, so y is not a function of x.

More generally, when you solve for y,

y=±√(3x²-4x-8),

so you always get two y-values - not allowed for a function!

You can also see that your equation is not a function when you graph it. You will get a hyperbola with two branches, which does not pass the so-called vertical line test: There are vertical lines that will intersect either branch of the hyperbola twice,
which cannot happen for the graph of a function.

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