write an equation for the function graphed below. the y intercept is at (0,0.2)

Explanation:

Step1: Identify vertical asymptotes

The vertical asymptotes are at $x = - 3$ and $x=3$. So the denominator of the rational - function is of the form $(x + 3)(x - 3)=x^{2}-9$.

Step2: Set up the general form of the rational function

Let the function be $y=\frac{a}{x^{2}-9}$.

Step3: Use the y - intercept to find the value of a

The y - intercept is at $(0,0.2)$. Substitute $x = 0$ and $y=0.2=\frac{1}{5}$ into $y=\frac{a}{x^{2}-9}$. We get $\frac{1}{5}=\frac{a}{0 - 9}$, then $a=\frac{-9}{5}=-1.8$.

Answer:

$y=\frac{-1.8}{x^{2}-9}$