Question

How do you graph `y=-3/(x+2)` using asymptotes, intercepts, end behavior?

Answer 1

Horizontal asymptote: y = 0. Vertical asymptote : `x=-2`.
y-intercept: -3/2

Explanation:

`(y-m_1x-c_1)(y-m_2x-c_2)= 0` represents the pair of lines

`y = m_1x+c_1 and y=m_2x+c_2`.

`(y-m_1x-c_1)(y-m_2x-c_2)= k` represents the hyperbola having the

pair of asymptotes

`(y-m_1x-c_1)(y-m_2x-c_2)= 0`

Here, it is

`y(x+2)=-3`

So, the asymptotes are given by

y = 0 and x+2=0.

graph{y(x+2)+3=0x^2 [-40, 40, -20, 20]}