assuming there are no reflections or dilations, explain how you would write the equation of the function…

Explanation:

Step1: Identify the parent - function

The graph resembles a reciprocal function $y = \frac{1}{x}$.

Step2: Determine the horizontal shift

The vertical asymptote is at $x=- 4$. For the parent - function $y=\frac{1}{x}$ with a vertical asymptote at $x = 0$, the horizontal shift $h=-4$. The general form of a shifted reciprocal function is $y=\frac{1}{x - h}$.

Step3: Write the function

Substituting $h=-4$ into $y=\frac{1}{x - h}$, we get $y=\frac{1}{x+4}$.

Answer:

$y=\frac{1}{x + 4}$