Please help!? Write an equation for a horizontal translation of y = 2/x. Then write an equation for a vertical translation of y = 2/x. Identify the horizontal and vertical asymptotes of the graph of each function.

Question

whpalmer4 · Answer

If you want to shift the equation right or left, you just add or subtract from the argument to the function.  For example, a parabola $y=x^2$ opens up, has its vertex at (0,0).  If we change the argument of $y = f(x) = x^2$ to $x-2$, then it becomes 
$$y = f(x-2) = (x-2)^2$$ and if you plot a few test points between  x =-2 and x = 2 you'll see that we've just shifted the parabola 2 units along the x-axis.  What originally happened at x =0 now happens at x = 2, and so on.  

For a vertical translation, that's just adding or subtracting from the result of the function.  Going back to our parabola, if we instead wanted to shift it up 2 units, we would write$$y = f(x)+2 = x^2 +2$$ and again plotting a few points will show that the parabola looks identical, except shifted upward 2 units.  In particular, the vertex now comes at (0,2) because $$y = x^2+2 = 0^2 + 2$$

So how would you translate your function in the two requested ways?