SOLUTION: y= {{{(x^3-3x^2-9x+27)/(x^2-9)}}}
For this problem, what would the vertical asymptote and removable discontinuity be? I am really confused :( please help me and thank you!!!
Algebra ->
Rational-functions
-> SOLUTION: y= {{{(x^3-3x^2-9x+27)/(x^2-9)}}}
For this problem, what would the vertical asymptote and removable discontinuity be? I am really confused :( please help me and thank you!!!
Log On
Question 430401: y=
For this problem, what would the vertical asymptote and removable discontinuity be? I am really confused :( please help me and thank you!!! Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! y=(x^3-3x^2-9x+27)/(x^2-9)
=(x^2(x-3)-9(x-3)/(x+3)(x-3)
=(x-3)(x^2-9)/(x+3)(x-3)
=(x^2-9)/(x+3)
=(x+3)(x-3)/(x+3)
=x-3
As you can see from the algebra and the graph below, the function became a straight line.
However, there are discontinuities in the line called "holes". Notice in the denominator of the original function there are two factors, (x+3) and (x-3). The function is undefined or not connected when either of these factors equal to zero, which they do when x=3 and x=-3.
Graphically, we should show tiny empty (as opposed to solid) dots in the line at x=3 and x=-3.
Hope this helps.
(