Analyze the graph of the function \( F(x)=\frac{x^{2}-12 x+32}{x^{2}-8 x+16} \).

The function \( F(x)=\frac{x^{2}-12x+32}{x^{2}-8x+16} \) does not have any specific domain restrictions based on the provided information. To determine the domain of the function, we need to consider the values of \( x \) for which the denominator is not equal to zero. The denominator of the function is \( x^{2}-8x+16 \). To find the values of \( x \) for which the denominator is not equal to zero, we need to solve the equation \( x^{2}-8x+16 = 0 \). Let's solve the equation \( x^{2}-8x+16 = 0 \) to determine the domain of the function. Solve the quadratic equation by following steps: - step0: Solve by factoring: \(x^{2}-8x+16=0\) - step1: Factor the expression: \(\left(x-4\right)^{2}=0\) - step2: Simplify the expression: \(x-4=0\) - step3: Move the constant to the right side: \(x=0+4\) - step4: Remove 0: \(x=4\) The solutions to the equation \( x^{2}-8x+16 = 0 \) are \( x = 4 \). This means that the denominator of the function is zero when \( x = 4 \), and the function is undefined at this point. Therefore, the domain of the function \( F(x)=\frac{x^{2}-12x+32}{x^{2}-8x+16} \) is all real numbers except \( x = 4 \).