Write an equation for the translation of y = 2/x that has the given asymptotes.
x = -7 and y = 3
To translate y = 2/x with x = -7 and y = 3 as the new asymptotes, we can use the form:
y = a/(x + 7) + 3
where "a" is a constant representing the stretch or compression of the graph. To find "a", we can use the fact that the original function y = 2/x has a horizontal asymptote at y = 0, which means the new graph must also have a horizontal asymptote at y = 0 after the translation. This occurs when:
lim┬(x→∞)〖(a/(x + 7) + 3)〗 = 0
Simplifying, we get:
a = 0
Therefore, the equation of the translation is:
y = 3/(x + 7)