Final answer:
To identify the asymptotes and state the end behavior of the function f(x) = 5x/(x - 25), we can start by looking at the denominator (x - 25). The vertical asymptote is x = 25, and the end behavior of the function is as x approaches positive infinity, f(x) approaches positive infinity, and as x approaches negative infinity, f(x) approaches negative infinity.
Step-by-step explanation:
To identify the asymptotes and state the end behavior of the function f(x) = 5x/(x - 25), we can start by looking at the denominator (x - 25). When the denominator is equal to zero, it would result in undefined values. So, the vertical asymptote of the function is x = 25. On the other hand, the numerator (5x) is a linear function, and the degree of the numerator is less than the degree of the denominator, which means that the end behavior of the function is determined by the denominator.
As x approaches positive infinity, the function approaches the vertical asymptote x = 25. And as x approaches negative infinity, the function approaches the same vertical asymptote x = 25. Therefore, the end behavior of the function is as follows: as x approaches positive infinity, f(x) approaches positive infinity, and as x approaches negative infinity, f(x) approaches negative infinity.