SOLUTION: How do I plot {{{f(x) = 4x - 3/x}}}? Why doesn't the y-intercept 0,0 work in this case?

Question 960716: How do I plot ? Why doesn't the y-intercept 0,0 work in this case?
Answer by josgarithmetic(39621) (Show Source): You can put this solution on YOUR website!
f is undefined at x=0, because denominators must not become zero.

You could make x y table of values, but you could also condense the function expression and evaluate a few things about it.

First notice that as x goes unbounded to the left or the right, f(x) will approach 4x, so this will be a slant asymptote, of y=4x.

Where is the numerator 0?

or , so these are critical points, as is x=0.

The three critical x values form intervals:

Evaluate the sign of f in each interval. That will help to determine if f is above or below the horizontal axis.

A vertical asymptote in addition to the slant asymptote, is x=0.
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