How do you find the domain, identify any horizontal, vertical, and slant (if possible) asymptotes and identify holes, x-intercepts, and y-intercepts for #(x^2-25)/(x^2+5x)#?

Answer 1

I'll give you only a partial answer:

The function can be rewritten as:

#=((x-5)(x+5))/(x*(x+5))#

We can cancel out the #(x+5)#'s BUT this we only do if #x!=-5# Also #x!=0# (both cases will make the numerator #=0#) So #x=0andx=-5#are points of interest.

The function turns into: #=(x-5)/x#

That (if #x# gets large enough) will converge to #x/x=1# graph{(x^2-25)/(x^2+5x) [-22.82, 22.81, -11.4, 11.42]}

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.