Write an equation for the translation of y = 4/x that has the given asymptotes.
15. x = 0,y = 3
16. x = 2,y = 2
For the translation of y = 4/x with asymptotes x = 0 and y = 3, we can use the general form of the equation for a hyperbola:
y = k + A/(x - h)
Where:
- (h, k) is the center of the hyperbola
- A is the vertical stretch factor
15. For the asymptotes x = 0, y = 3, we have:
h = 0, k = 3
So the equation for the translated hyperbola is:
y = 3 + 4/x
16. For the asymptotes x = 2, y = 2, we have:
h = 2, k = 2
So the equation for the translated hyperbola is:
y = 2 + 4/(x - 2)