Questions: Write an equation for the function graphed below

Transcript text: Write an equation for the function graphed below

Solution

Solution Steps

Step 1: Identify the Vertical Asymptotes

The graph has vertical asymptotes at \( x = -2 \) and \( x = 4 \). This suggests that the function has factors in the denominator that become zero at these points.

Step 2: Identify the Horizontal Asymptote

The graph does not have a horizontal asymptote, but it appears to have a slant asymptote. This suggests that the degree of the numerator is one more than the degree of the denominator.

Step 3: Determine the Form of the Function

Given the vertical asymptotes and the slant asymptote, the function can be written in the form: \[ f(x) = \frac{ax + b}{(x + 2)(x - 4)} \]

Final Answer

The equation for the function graphed is: \[ f(x) = \frac{ax + b}{(x + 2)(x - 4)} \] To find the specific values of \(a\) and \(b\), we would need additional points from the graph.

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