Graphing/function help!!

Question

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!

Answer 1

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. Since

 

y²≥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.

 

 

 

Answer 2

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!

 

y^2 = 3x^2 -4x -8

You can take the square root of each side.  Then, use a graphing calculator or x/y chart to graph the equation.

 

I hope this helps.

 

Answer 3

Erica,

   One way to visualize the function is to assume values for x and see the values of y that are derived.

The function is y² = 3x² -4x -8.

For x = 0, y² = -8. Here the answer is not a real number. 

If x = 1, y² = 3-4-8 = -9; again not a real number.

If x = 3, y² = 27-12-8 = 7; here the answer is a real number.

  Real answers for this function exist when y² is 0 or positive. If your aim is to determine if the function is real for all values of x, then that is not the case.

  Your graphing calculator will be able to plot real values for the function after you input the function into it. Hope this helps with your understanding of the problem.