Find the holes in the graph of the rational function \(f(x) = \frac{x^2 - 4}{x - 2}\).
Answer
Step 4: The function \(f(x) = x + 2\) is defined for all values of x except x = 2. So, the hole in the graph of the function is at x = 2.
Step 1 ：Step 1: Factor the numerator and the denominator of the function. \(f(x) = \frac{(x - 2)(x + 2)}{x - 2}\).
Step 2 ：Step 2: Cancel out the common factors in the numerator and the denominator. After cancellation, we get \(f(x) = x + 2\).
Step 3 ：Step 3: The original function is undefined when the denominator equals zero. So, find the value of x that makes the denominator zero. \(x - 2 = 0 \Rightarrow x = 2\).
Step 4 ：Step 4: The function \(f(x) = x + 2\) is defined for all values of x except x = 2. So, the hole in the graph of the function is at x = 2.
