How do you graph #f(x)=3/x+1# using holes, vertical and horizontal asymptotes, x and y intercepts?

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Somebody N.
Dec 5, 2017

See below.

Explanation:

y axis intercepts occur when #x=0#. #x=0# is undefined for this function, so no y intercept.

x axis intercepts occur when #y=0#:

#3/x+1=0=>x=-3#

Coordinate: #( -3 , 0 )#

as #x->oo# , #color(white)(888)3/x+1->1#

as #x->-oo# , #color(white)(888)3/x+1->1#

The line #y=1# is a horizontal asymptote.

as #x->0^+# , #color(white)(888)3/x+1->oo#

as #x->0^-# , #color(white)(888)3/x+1->-oo#

The line #x=0# is a vertical asymptote.

Graph:

enter image source here

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