# What is an equation for the translation y = 4/x that has the given asymptotes. x = 4, y = -3?

Jan 15, 2018

$y = \frac{4}{x - 4} - 3$

#### Explanation:

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If you subtract a constant from your $x$ in the original function you shift the graph in the positive direction by that number of units.

And if you subtract a constant from your $y$ in the original function you move its graph down by that number of units.

Your original function was $y = \frac{4}{x}$. When you solve for the root of the denominator, you find the vertical asymptote. In this case, it is $x = 0$, i.e. the $y$-axis.

And when $x$ goes to $\infty$, $y = \frac{4}{\infty} = 0$ which means your horizontal asymptote is $y = 0$, i.e. the $x$-axis. Here is the graph:

Now, you can see the transformation of $y = \frac{4}{x}$ below. As is evident, it has shifted $4$ units to the right and $3$ units down with vertical asymptote at $x = 4$ and horizontal asymptote at $y = - 3$.

Jan 15, 2018

translation of 4 units right
translation of 3 units down
$y = \frac{4}{x - 4} - 3$

#### Explanation:

translation of 4 units right
translation of 3 units down

$y = f \left(x\right) \to y = f \left(x - 4\right) - 3$
$y = \frac{4}{x - 4} - 3$

I hope it helps :)