college algebra for calculus. polynomial and rational functions

[unknownfly]

Hello I need some help with this problem f(x)=x^2-4x/x+4
I need to simplify and graph it (label restrictions, zeros, and asymptotes) and I know it has a verticle asymptote at x=-4 and an oblique asymptote at y=x-8

 

[Prof]

You should tell us what sort of calculator you are allowed to use for this question. Here are some ideas for the next steps. Your vertical asymptote (VA) equation is correct. Graph that as a broken line (all points where x = -4). The graph will go way up or down just before a VA and come down from infinity or up from negative infinity just after a VA. You can substitute x -values slightly less and slightly more than -4 to determine if the graph is approaching a y of infinity or negative infinity on each side of the VA. Zeroes refer to when g(x) or y = 0. Factor the fraction numerator and determine what x-values make the fraction equal zero. These are the zeroes. You should get two of them. Once you find them, plot those two points on your graph.

 

[Otis]

… need some help with … f(x)=(x^2-4x)/(x+4)
… simplify and graph it (label restrictions, zeros, and asymptotes)
… I know [the asymptotes]

Hi unknownfly. First a note about notation. When we type rational expressions, we need to use grouping symbols around numerators and denominators (as shown above). I'm not sure what they mean, by simplifying the given function; maybe they want to see the numerator factored. I'm thinking "restrictions" means a domain statement.

Is finding the zeros what you need help with?

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