Question

Write the equation for the translation of y= 7/x that has asymptotes at x=-3 and y = 17

Answer 1

Translate 7/x to the left by 3 and up by 17 to get:

y = 17 + 7/(x+3)

Answer 2

Let us consider the given function
`y=(7)/(x)`,

It has a vertical asymptote at x=0, because x=0 makes the denominator 0, which is not defined.

To have the vertical asymptote at x= -3, the denominator has to be x-(-3), or x+3.

So, the function
`y=(7)/(x+3)` has vertical asymptote at x = -3.

Since, the function
`y=(7)/(x+3)` has a horizontal asymptote at y=0.

So, to get the horizontal asymptote at y=17 we have to add 17 to the function.

Therefore, the function
`y=(7)/(x+3)+17` has a vertical asymptote at x = -3 and a horizontal asymptote at y = 17.

So, Equation after the translation is:

`y=(7)/(x+3)+17`.