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$$h(x) = \frac{6x^2}{3x^2-2x-1}$$

I know that the domain is excluding $-\frac{1}{3}$ and $1$.

The range is $(2, \infty)$ and $(-\infty, 0)$

How many minimum values need to be plotted in order to find the range of a function?

Like say there's an equation and its range is all values up to 1000. It would be a lot of work to do that on a graph by hand. Is there a shortcut?

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    Do you intend for the $3x^{2x} - 1$ all to be in the denominator of the fraction? What you have done parses, but it is not great style.2012-07-27
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    Do you mean the domain is between $-\frac 13$ and $1$? The denominator is negative in that range. The domain can't include $-\frac 13$ and $1$, but it can include the rest of the reals.2012-07-27
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    I find a local minimum at $(-1,\frac 32)$ outside your claimed range2012-07-27

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