How do you graph #f(x)= (x^2-100)/(x+10)#?

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Answer 1 · 2015-06-28T16:08:06

#f(x) = (x^2-100)/(x+10) = ((x-10)(x+10))/(x+10) = x-10#

with excluded value #x=-10#.

This is a straight line of slope #1# passing through #(0, -10)# and #(10, 0)# with excluded point #(-10, -20)#

#f(x) = (x^2-100)/(x+10)#

#= ((x-10)(x+10))/(x+10)#

#= x-10#

with exclusion #x!=-10#.

The graph of #f(x)# is like the graph of #x-10# except that #f(x)# is not defined at the point #(-10, -20)#

All the limits as you approach that point behave well, it's just that #f(-10)# is undefined as it's equal to #0/0#.

graph{(x^2-100)/(x+10) [-37.5, 42.5, -24, 16]}