How to deduce the function from the graph?
It is given that the degree of numerator of f(x) is 2
** My Attempt**
There are two asymptotes so the denominator should be in the form $k(x+2)(x-1)$. And I can see there are two stationary points on the graph at $x=-5,x=-1$But I'm confused on how to use this in deducing function of the graph. Any hint would be highly appreciated!
Hint: there is a single root at $x=-3$ and the numerator must be of order less that the denominator since the $x$ axis is an asymptote. Hence the function will be of the form
$$y=\frac{\lambda(x+3)}{(x+2)(x-1)}$$
If you differentiate this you will indeed find the correct $x$ values for the given stationary points so you just have to determine the value of $\lambda$.
Can you finish?