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 $y=\frac{7}{x}$,

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 $y=\frac{7}{x+3}$ has vertical asymptote at x = -3.

Since, the function $y=\frac{7}{x+3}$ 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 $y=\frac{7}{x+3}+17$ has a vertical asymptote at x = -3 and a horizontal asymptote at y = 17.

So, Equation after the translation is:

$y=\frac{7}{x+3}+17$.