13. Sketch: $$ R(x)=\frac{2 x-4}{x-4} $$. Graph any asymptotes (dashed) and intercepts i) Find $$ x $$ and $$ y $$ intercepts: ii) Vertical asymptote: iii) Horizontal asymptote: iv) Determine the behavior of the graph of $$ R $$ on either side of the vertical asymptote: v) Sketch detailed graph.

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It seems that I am unable to create a visual graph directly. However, I can guide you on how to sketch it based on the information we have gathered.

### Steps to Sketch the Graph of $$ R(x) = \frac{2x - 4}{x - 4} $$:

1. **Draw the Axes:**
   - Draw the horizontal axis (x-axis) and the vertical axis (y-axis).

2. **Plot the Intercepts:**
   - Mark the $$ x $$-intercept at $$ (2, 0) $$.
   - Mark the $$ y $$-intercept at $$ (0, 1) $$.

3. **Draw the Asymptotes:**
   - Draw a dashed vertical line at $$ x = 4 $$ (vertical asymptote).
   - Draw a dashed horizontal line at $$ y = 2 $$ (horizontal asymptote).

4. **Behavior Near the Asymptotes:**
   - As $$ x $$ approaches 4 from the left, the graph goes down towards $$ -\infty $$.
   - As $$ x $$ approaches 4 from the right, the graph goes up towards $$ +\infty $$.

5. **Sketch the Curve:**
   - For $$ x < 4 $$, the graph will be below the horizontal asymptote $$ y = 2 $$ and will cross the $$ x $$-axis at $$ (2, 0) $$.
   - For $$ x > 4 $$, the graph will rise above the horizontal asymptote $$ y = 2 $$.

6. **Final Touches:**
   - Ensure the graph approaches the horizontal asymptote $$ y = 2 $$ as $$ x $$ goes to $$ \pm \infty $$.

### Summary of the Graph:
- The graph will have a $$ x $$-intercept at $$ (2, 0) $$ and a $$ y $$-intercept at $$ (0, 1) $$.
- It will have a vertical asymptote at $$ x = 4 $$ and a horizontal asymptote at $$ y = 2 $$.
- The graph will show a clear transition from $$ -\infty $$ to $$ +\infty $$ at the vertical asymptote.

By following these steps, you should be able to create a detailed sketch of the function $$ R(x) $$. If you have graphing software or a graphing calculator, you can also input the function directly to visualize it.
To sketch the function $$ R(x) = \frac{2x - 4}{x - 4} $$, follow these steps: 1. **Intercepts:** - $$ x $$-intercept: $$ (2, 0) $$ - $$ y $$-intercept: $$ (0, 1) $$ 2. **Asymptotes:** - Vertical asymptote: $$ x = 4 $$ - Horizontal asymptote: $$ y = 2 $$ 3. **Behavior:** - As $$ x $$ approaches 4 from the left, $$ R(x) $$ approaches $$ -\infty $$. - As $$ x $$ approaches 4 from the right, $$ R(x) $$ approaches $$ +\infty $$. 4. **Graph:** - Plot the intercepts and asymptotes. - Draw the graph approaching the asymptotes and passing through the intercepts. This will give you a clear sketch of the function's behavior.

Sketch: . Graph any asymptotes (dashed) and intercepts
i) Find and intercepts:
ii) Vertical asymptote:
iii) Horizontal asymptote:
iv) Determine the behavior of the graph of on either side of the vertical asymptote:
v) Sketch detailed graph.

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Steps to Sketch the Graph of :

Summary of the Graph:

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Sketch: . Graph any asymptotes (dashed) and intercepts i) Find and intercepts: ii) Vertical asymptote: iii) Horizontal asymptote: iv) Determine the behavior of the graph of on either side of the vertical asymptote: v) Sketch detailed graph.