Problem

Suppose that $f(x)=\frac{x-4}{(x-6)(x+8)}$
a. What is the vertical intercept for $f$ ?
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b. List the horizontal intercepts for $f$.
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Answer

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Answer

Final Answer: The vertical intercept for \(f\) is \(\boxed{\frac{1}{12}}\)

Steps

Step 1 :The vertical intercept of a function is the point where the graph of the function intersects the y-axis. This occurs when x = 0. So, to find the vertical intercept, we need to substitute x = 0 into the function and solve for y.

Step 2 :Substitute x = 0 into the function: \(f = \frac{x - 4}{(x - 6)(x + 8)}\)

Step 3 :Solve for y: \(y = \frac{1}{12}\)

Step 4 :Final Answer: The vertical intercept for \(f\) is \(\boxed{\frac{1}{12}}\)

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