SOLUTION: Consider the function {{{ f(x)= (x^2+3x-4)/(x^2+9x+20) }}} Using algebra only (not a graphing calculator), find the following features of the graph. a) x-intercept(s) b) vertica

Algebra ->  Rational-functions -> SOLUTION: Consider the function {{{ f(x)= (x^2+3x-4)/(x^2+9x+20) }}} Using algebra only (not a graphing calculator), find the following features of the graph. a) x-intercept(s) b) vertica      Log On


   



Question 972885: Consider the function +f%28x%29=+%28x%5E2%2B3x-4%29%2F%28x%5E2%2B9x%2B20%29+
Using algebra only (not a graphing calculator), find the following features of the graph.
a) x-intercept(s)
b) vertical asymptote(s)
c) horizontal asymptote(s)
d) removable discontinuity (“hole”)
I already found a-c, I just need help with d. I had said that x+5=0 so x=-5, therefore the domain is all real #'s but -5, but that was wrong. Please help, thank you!

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Just help for (d), holes in the graph.

+f%28x%29=+%28x%5E2%2B3x-4%29%2F%28x%5E2%2B9x%2B20%29+

%28%28x-1%29%28x%2B4%29%29%2F%28%28x%2B4%29%28x%2B5%29%29
an obvious factor of 1 is present, making the function undefined for x=-4.

You did not identify the correct factor of 1 when you picked the "hole" at x=-5.