Y=8x-3/-4x-10 has a vertical asymptote with equation(enter equation of the vertical asymptote

Accepted Solution

Answer:x=-2.5 if the function is [tex]f(x)=\frac{8x-3}{-4x-10}[/tex] Step-by-step explanation:[tex]y=\frac{8x-3}{-4x-10}[/tex] has discontinuities when the denominator is 0.You will either have a hole or a vertical asymptote depending on what happens to the numerator after you find when the bottom is 0.That is whatever you found that makes the bottom 0, if it makes the top also 0 then you will have a hole at x=the number that made the bottom 0.If it makes the top anything other than 0, then it is a vertical asymptote at x=the number you found that made the bottom 0.Let's do this now.When is -4x-10 equal to 0?We have to solve the equation:-4x-10=0Add 10 on both sides:-4x=10Divide both sides by -4:x=10/-4Reduce by dividing top and bottom by 2:x=5/-2x=-5/2orx=-2.5 Β (if you want decimal form)Now does it make the top 0? This is the deciding factor on whether you have a hole at x=-2.5 or a vertical asymptote at x=-2.5.Let's see.8(-2.5)-3=-23 Since the top is not 0 at x=-2.5 then you have a vertical asymptote at x=-2.5.If the top were 0, then you would have had a hole at x=-2.5.