Question

Найдите вертикальную и горизонтальную асимптомы графика функции f(x)=2/2-x​

Answer 1

Ответ:

Объяснение:

гориз. у=0,  вертик. х=2

Answer 2

Vertical and Horizontal Asymptotes of the Function f(x) = 2/(2-x)

To find the vertical and horizontal asymptotes of the function f(x) = 2/(2-x), let's analyze the behavior of the function as x approaches certain values.

Vertical Asymptotes: Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a certain value. In this case, we need to find the values of x for which the denominator of the function becomes zero.

Setting the denominator, 2-x, equal to zero and solving for x, we get: 2 - x = 0 x = 2

Therefore, there is a vertical asymptote at x = 2.

Horizontal Asymptotes: Horizontal asymptotes occur when the function approaches a constant value as x approaches positive or negative infinity. To find the horizontal asymptote, we need to analyze the behavior of the function as x approaches infinity and negative infinity.

As x approaches infinity, the function becomes: f(x) = 2/(2 - x) Since the degree of the numerator and denominator is the same (both are 1), we can compare the leading coefficients. The leading coefficient of the numerator is 2, and the leading coefficient of the denominator is -1. Therefore, as x approaches infinity, the function approaches 2/(-1) = -2.

As x approaches negative infinity, the function becomes: f(x) = 2/(2 - x) Again, comparing the leading coefficients, we find that as x approaches negative infinity, the function approaches 2/(-1) = -2.

Therefore, there is a horizontal asymptote at y = -2.

To summarize: - Vertical asymptote: x = 2 - Horizontal asymptote: y = -2

Please note that the analysis above is based on the given function f(x) = 2/(2-x) and the behavior of the function as x approaches certain values.