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The graph shown suggests we need to find the rational function by analyzing the following key features:

1. **Vertical asymptotes:** These occur where the denominator of the rational function equals zero. Based on the graph, we can see vertical asymptotes at \(x = -2\) and \(x = 4\). This suggests factors in the denominator of the form \((x + 2)\) and \((x - 4)\).

2. **Horizontal asymptote:** There seems to be a horizontal asymptote at \(y = 0\), which suggests the degree of the numerator is less than or equal to the degree of the denominator.

3. **Behavior near vertical asymptotes:** 
   - At \(x = -2\), the graph approaches positive infinity on the left and negative infinity on the right.
   - At \(x = 4\), the graph approaches negative infinity on the left and positive infinity on the right.
   
4. **Zeros of the function:** The graph crosses the x-axis at \(x = 2\), suggesting a zero at \(x = 2\). This means the numerator contains a factor \((x - 2)\).

### Possible Rational Function
From this, we can hypothesize that the function is of the form:

\[
f(x) = \frac{a(x - 2)}{(x + 2)(x - 4)}
\]

### Determining the constant \(a\):
- We also observe a point passing through \((x = 6, y = -1)\) on the graph. Substituting \(x = 6\) and \(y = -1\) into the function will allow us to solve for \(a\).

Let's calculate the value of \(a\).

Find the rational function whose graph is shown in the figure below.

This rational function problem focuses on analyzing vertical asymptotes, horizontal asymptotes, and the zero of the function. The graph shows vertical asymptotes at x = -2 and x = 4, with the function crossing the x-axis at x = 2. Learn to solve this with key mathematical concepts such as rational functions and asymptotes.

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