Graph the rational function. $$ f(x)=\frac{-4}{-x-4} $$ Start by drawing the vertical and horizontal asymptotes. Then

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1. **Simplify the function**

The given function is
   $$
   f(x)=\frac{-4}{-x-4}.
   $$
   Multiply the numerator and denominator by $$-1$$ to obtain an equivalent form:
   $$
   f(x) = \frac{4}{x+4}.
   $$

2. **Determine the Vertical Asymptote**

The vertical asymptote occurs when the denominator is zero (and the numerator is nonzero). Set
   $$
   x+4=0.
   $$
   Solving, we find
   $$
   x = -4.
   $$
   Thus, the vertical asymptote is the line
   $$
   x = -4.
   $$

3. **Determine the Horizontal Asymptote**

For rational functions, the horizontal asymptote is found by comparing the degrees of the numerator and denominator. Here, the numerator is a constant (degree 0) and the denominator is linear (degree 1). Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is
   $$
   y = 0.
   $$

4. **Plot Additional Key Points**

To help in sketching the graph, find the $$y$$-intercept by setting $$x=0$$:
   $$
   f(0)=\frac{4}{0+4}=\frac{4}{4}=1.
   $$
   So, the $$y$$-intercept is at $$(0,1)$$.

5. **Sketching the Graph**

- First, draw the vertical asymptote as a dashed line at
     $$
     x = -4.
     $$
   - Next, draw the horizontal asymptote as a dashed line at
     $$
     y = 0.
     $$
   - Plot the point $$(0,1)$$ on the graph.
   - The hyperbola given by $$ f(x)=\frac{4}{x+4} $$ will approach the vertical asymptote $$ x = -4 $$ without touching it, and it will approach the horizontal asymptote $$ y=0 $$ as $$ x $$ goes to positive or negative infinity.

The graph will consist of two branches:

- For $$ x > -4 $$, the function is positive since both the numerator and denominator are positive, and the graph will approach $$ y=0 $$ as $$ x $$ increases.
   - For $$ x < -4 $$, the denominator is negative, so the function is negative; the graph will approach $$ y=0 $$ as $$ x $$ decreases, and will tend to negative infinity as $$ x $$ approaches $$-4$$ from the left.

This completes the step-by-step process of determining the asymptotes and key features for graphing the function.
To graph the function $$ f(x) = \frac{-4}{-x-4} $$, first simplify it to $$ f(x) = \frac{4}{x+4} $$. Then, draw the vertical asymptote at $$ x = -4 $$ and the horizontal asymptote at $$ y = 0 $$. Plot the $$ y $$-intercept at $$ (0,1) $$ and sketch the hyperbola branches approaching the asymptotes accordingly.

Graph the rational function. \[ f(x)=\frac{-4}{-x-4} \] Start by drawing the vertical and horizontal asymptotes. Then

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