SOLUTION: I would appreciate help with this problem. Write an equation for the translation of y=4/x that has the asymptotes x=7 and x=6. I tried using the method in my Algebra 2 book,

Algebra ->  Rational-functions -> SOLUTION: I would appreciate help with this problem. Write an equation for the translation of y=4/x that has the asymptotes x=7 and x=6. I tried using the method in my Algebra 2 book,      Log On


   

Question 415324: I would appreciate help with this problem.
Write an equation for the translation of y=4/x that has the asymptotes x=7 and x=6.
I tried using the method in my Algebra 2 book, but it doesn't really explain how to do it. Thanks.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
did you mean x = 7 and y = 6 ?????

the equation is shown below with asymptotes at x = 0 and y = 0

graph%28600%2C600%2C-30%2C30%2C-30%2C30%2C4%2Fx%29

add 6 to the equation to move the y asymptote to y = 6.

graph%28600%2C600%2C-30%2C30%2C-30%2C30%2C4%2Fx+%2B+6%29

subtract 7 from the denominator in the equation to move the x asymptote to 7.

graph%28600%2C600%2C-30%2C30%2C-30%2C30%2C4%2F%28x-7%29+%2B+6%29

your final equation is 4/(x-7) + 6.

i'm not totally sure this is what you want, but it looks like it might be.

your vertical asymptote occurs when the denominator in the equation is equal to 0.

if the denominator is equal to x, then the vertical asymptote is equal to 0.

if the denominator is equal to (x-7), then the vertical asymptote is equal to 7 because 7-7 = 0.

your horizontal asymptote occurs when the value of y approaches a number other than infinity as the value of x approaches infinity.

in the equation y = 4/(x-7) we already made the vertical asymptote equal to 7.

as the value of x approaches infinity, the value of (x-7) also approaches infinity.

as the value of (x-7) approaches infinity, the value of y = 4/(x-7) approaches 0.

if we want the value of y to approach 6 as the value of (x-7) approaches infinity, then we need to add 6 to the equation to get:

y = 4/(x-7) + 6