For what values of x, if any, does #f(x) = 1/((5x+8)(x+4) # have vertical asymptotes?

1 Answer
Anish M.
Mar 22, 2018

#x# = #-4# and #-8/5#

Explanation:

So, a vertical asymptote is a line that extends vertically to infinity. If we notice, it implies that the y co-ordinate of the curve much reach Infinity.

We know that infinity = #1/0#

So, when compared with #f(x)#, it implies that the denominator of #f(x)# should be zero. Hence,

#(5x+8)(x+4)# = #0#

This is a quadratic equation whose roots are #-4# and #-8/5#.

Hence, at #x# = #-4#, #-8/5# we have vertical asymptotes

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