Question

Find all horizontal and vertical asymptotes (if any). s(x)={2x+3}/{x-1}

Answer 1

The horizontal asymptote is y = 2 and the vertical asymptote is x = 1.

Step-by-step explanation:

To find the horizontal asymptote of the function s(x) = (2x+3)/(x-1), we need to determine what happens to the function as x approaches positive infinity and negative infinity. As x approaches infinity, the non-zero x term will dominate the function, so the horizontal asymptote is y = 2. As x approaches negative infinity, the x term will also dominate the function, so the horizontal asymptote is again y = 2.

To find the vertical asymptote, we need to determine where the function is undefined. In this case, the function is undefined when the denominator (x-1) is equal to zero. Therefore, the vertical asymptote is x = 1.