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# Range of fractional functions watch

1. Hi
How do you find the range of fractional functions e.g f(x) = 5x/x^1+1 ?

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2. Do you mean this: ?

You could try finding the minimum and maximum of that function (when you differentiate and set =0).
You could also try trial-and-error and put numbers in your calculator to see what is happening, and try and make little sketch.
3. this example is where the denominator is defined for all x - so you know theres no problem with vertical asymptotes.

For this particular example, y is at its maximum and minimum when x is at its lowest possible minimum :

For most other rational functions, you`d have to examine the behaviour of y as x approached +/- infinity and the vertical asymptotes.
4. Put the function as y=f(x), take the denominator on the left hand side to basically form a quadratic in terms of x. Put the condition that all roots of the quadratic must be real to obtain a range for y(always works )

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Updated: January 16, 2015
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