What's the equation for this?

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Answer 1 · 2018-01-07T19:32:07

#y = (x-4)/(x^2-16)#

There is a vertical asymptote at x = -4 and a horizontal asymptote at y = 0 means:

#y = 1/(x+4)#

There is a removable discontinuity at #x = 4# means there is a common factor in the numerator and denominator of #x-4#:

#y = 1/(x+4)*(x-4)/(x-4)#

#y = (x-4)/(x^2-16)#

Check that the y intercept is #(0,1/4)#

#y = (0-4)/(0^2-16)#

#y = 1/4#

This checks