How do you find the asymptote and graph $y=1/(x-5)-4$ ?

Question

6186 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-02T02:54:11

$y$ has a vertical asymptote of $x=5$ and a horizontal asymptote of $y=-4$
Graph below.

$y= 1/(x-5)-4$

Notice $y$ is undefined at $x=5$

Consider, $lim_(x->5^-) y = -oo and lim_(x->5^+) y = +oo$

Also, $lim_(x->-oo) y = -4 and lim_(x->+oo) y = -4$

Hence $y$ is a rectangular hyperbola with a vertical asymptote of $x=5$ and a horizontal asymptote of $y=-4$

The graph of $y$ is shown below.

graph{1/(x-5)-4 [-5.42, 17.08, -7.105, 4.14]}

How do you find the asymptote and graph y=1/(x-5)-4y=1/(x-5)-4?