Problem

Find the holes in the graph of the function \(f(x) = \frac{x^2 - 9}{x - 3}\).

Solution

Step 1 :Step 1: Simplify the function, \(f(x) = \frac{x^2 - 9}{x - 3}\), by factoring the numerator to get \(f(x) = \frac{(x - 3)(x + 3)}{x - 3}\).

Step 2 :Step 2: Cancel out the common factor \((x - 3)\) in the numerator and the denominator to get \(f(x) = x + 3\).

Step 3 :Step 3: Determine the value of \(x\) that makes the original denominator zero since this value of \(x\) will be a hole in the graph. In this case, \(x - 3 = 0\) implies that \(x = 3\) is a hole.

Step 4 :Step 4: To find the y-coordinate of the hole, substitute \(x = 3\) into the simplified function \(f(x) = x + 3\) to get \(f(3) = 3 + 3 = 6\).

From Solvely APP
Source: https://solvelyapp.com/problems/MNECcYj8Rp/

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