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

Answer 1

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

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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Answer 2

Scarlett Allison

The function f(x) = 1/((5x+8)(x+4) has vertical asymptotes at x = -8/5 and x = -4.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.