The given function y=4/x has a vertical asymptote at x=0 and a horizontal asymptote at y=0. To translate the function to have asymptotes x=7 and y=6, we can use the following form of the equation:
y = a * (4 / (x - h)) + k
where h and k are the horizontal and vertical shift respectively, and a is a scaling factor.
To make the vertical asymptote at x=7, we need to shift the function horizontally by 7 units to the right. So, h=7.
To make the horizontal asymptote at y=6, we need to shift the function vertically by 6 units upwards. So, k=6.
The scaling factor a can be chosen based on the desired behavior of the function around the asymptotes. Since the original function y=4/x approaches zero as x goes to infinity or negative infinity, and since we want the same behavior for the translated function, we can choose a=4/7.
Putting these values into the equation, we get:
y = (4/7) * (4 / (x - 7)) + 6
Simplifying this equation, we get:
y = (16 / (7x - 49)) + 6
This is the equation for the translation of y=4/x that has asymptotes x=7 and y=6.
Write an equation for the translation of y=4/x that has the asymptotes x=7 and y=6
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