Write an equation for the translation of y=(4/x) that has asymptotes x=7and y=6.
To translate the equation y=(4/x) to have asymptotes x=7 and y=6, we can use the equations of the vertical and horizontal asymptotes to determine the transformation.
The equation of the vertical asymptote x=7 means that the new equation will have a vertical asymptote at x=7. To move the asymptote from x=0 to x=7, we need to add 7 to x in the equation. So, the x-coordinate of the transformed equation will be (x+7).
The equation of the horizontal asymptote y=6 means that the new equation will have a horizontal asymptote at y=6. To move the asymptote from y=0 to y=6, we need to add 6 to y in the equation. So, the y-coordinate of the transformed equation will be (y+6).
Putting it all together, the equation for the translation of y=(4/x) with asymptotes x=7 and y=6 can be written as:
(y+6) = 4/(x+7)