Question

Write an equation for the function graphed below. The y intercept is at (0,0.3)

Answer 1

Notice that the graph has two vertical asymptotes at x= - 1 and x=3, also when x tends to 3 the graph tends to infinity, and the function has x=1 as a double root, therefore the function has to have the following form ( not yet the exact function):

$y=\frac{k(x-1)^2}{(x-3)^2(x+1)}$

Now, to compute the value of k we use the y-intercept,

$\begin{gathered} 0.3=\frac{k(0-1)^2}{(0-3)^2(0+1)}=\frac{k}{9} \\ k=0.3\cdot9=2.7 \end{gathered}$

Finally, the equation for the function graphed is:

$y=\frac{2.7(x-1)^2}{(x-3)^2(x+1)}$