`y=(x^2-5x-36)/(3x)` Graph the function.

We are asked to graph the function `y=(x^2-5x-36)/(3x) ` :

Factoring the numerator yields:

`y=((x-9)(x+5))/(3x) `

There is a vertical asymptote at x=0 (and thus no y-intercept.)

The x-intercepts are 9 and -5.

The slant asymptote (found by division) is y=1/3x-5/3.

The first derivative is positive for all x in the domain so the function is increasing on its domain.

The graph:

Comments

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