Which of the following is the function represented by the graph? y=(1)/((x+3))-5 y=(1)/((x-3))+5 y=(1)/((x+5))-3 y=(1)/((x-5))+3 Consider the graph below. s x 5 -5

Based on the description of the graph, we can analyze the behavior of the curves to determine which function it represents.1. The first curve is in the second quadrant, monotonically decreasing. As x approaches -2, y approaches positive infinity. This suggests a vertical asymptote at x = -2, which means the function has a denominator of (x + 2).2. The second curve is in the first and fourth quadrants, monotonically decreasing. As x approaches 2, y approaches positive infinity. This suggests a vertical asymptote at x = 2, which means the function has a denominator of (x - 2).3. The third curve is in the first quadrant, monotonically decreasing. As x approaches 3, y approaches positive infinity. This suggests a vertical asymptote at x = 3, which means the function has a denominator of (x - 3).Now, let's analyze the given options:A) \(y=\frac{1}{(x+3)}-5\)This function has a vertical asymptote at x = -3, which does not match any of the described curves.B) \(y=\frac{1}{(x-3)}+5\)This function has a vertical asymptote at x = 3, which matches the third curve's behavior. However, the "+5" would shift the curve upwards, which is not mentioned in the description.C) \(y=\frac{1}{(x+5)}-3\)This function has a vertical asymptote at x = -5, which does not match any of the described curves.D) \(y=\frac{1}{(x-5)}+3\)This function has a vertical asymptote at x = 5, which does not match any of the described curves.None of the given options perfectly match the description of the graph provided. However, based on the information given, the closest match would be option B, \(y=\frac{1}{(x-3)}+5\), because it has a vertical asymptote at x = 3, which corresponds to the third curve's behavior. The "+5" would not match the description exactly, but since none of the options are a perfect fit, we would choose the one that matches the most characteristics described.Final Answer: \(y=\frac{1}{(x-3)}+5\) (with the caveat that this does not perfectly match the description provided).