Question

Please how do I sketch the graph of x^2/x+1

Answer 1

well, this is a rather messier function, and is not just easily plotted with some linear form or something. so if i were to sketch this, i would try to use some of the first,2nd,and3rd derivative laws to attain a rough sketch,,,, do you know how to use derivatives to sketch graphs?

Answer 2

no I do not.

Answer 3

check this out! when i was in calc 1 some years ago, this guy Paul really helped me with every topic. and its all layed out nicely. http://tutorial.math.lamar.edu/Classes/CalcI/CriticalPoints.aspx it is exactly what you want to do!

Answer 4

It's a rational function, so you can at least find horizontal and vertical asymptotes, and plot a few points to see where it does and doesn't live.

Answer 5

+1 to chemENGINEER for Paul's Online Math Notes!

Answer 6

About those asymptotes, though, the denominator is x+1, and there's nothing on top to cancel it out, so there is going to be a vertical asymptote at x=-1.
When you divide to find the quotient, you get y=x-x/(x+1). The -x/(x+1) approaches -1 quickly, so for extreme values of x, the curve is going to approach the slant asymptote of y=x-1. You can also see that it passes through the point (0,0) and that is the only zero of the function.
select a couple other x's and plug them in to plot a few points and flesh it out.
No calculus required.

Answer 7

@Hollywood_chrissy
Does that make sense?

Answer 8

yes