What are the equations of the vertical and the horizontal asymptotes of the graph of $y=\frac{1}{x-2}+4$ ?
Answer
Final Answer: The vertical asymptote of the graph of \(y=\frac{1}{x-2}+4\) is \(x=2\) and the horizontal asymptote is \(y=4\). So, the final answer is \(\boxed{x=2, y=4}\).
Step 1 ：Set the denominator equal to zero and solve for x to find the vertical asymptote: \(x-2=0\) which gives \(x=2\).
Step 2 ：Determine the horizontal asymptote by looking at the degree of the numerator and the denominator. Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is the constant term of the function, which is \(y=4\).
Step 3 ：Final Answer: The vertical asymptote of the graph of \(y=\frac{1}{x-2}+4\) is \(x=2\) and the horizontal asymptote is \(y=4\). So, the final answer is \(\boxed{x=2, y=4}\).
