Question

Write an equation for the translation of y=6/x that has the asymptotes x = 4 and y = 5

Answer 1

Answer:

$\displaystyle y=\frac{30x}{6(x-4)}$

Step-by-step explanation:

Keep in mind that a rational function with a vertical asymptote at $x=4$ means the denominator must be 0 when $x=4$ is plugged in.

This means we have $\displaystyle y=\frac{6}{x-4}$ so far.

To account for the horizontal asymptote at $y=5$, we need to adjust the numerator and denominator so that they are the same degree and that the leading coefficients have a ratio of 5. We can do this by multiplying the numerator by 5x and the denominator by 6.

This leaves us with $\displaystyle y=\frac{30x}{6(x-4)}$ as the translated equation since the end behavior of the function is $\displaystyle y=\frac{30x}{6x}=5$. See attached graph.