Question

Which of the following describes the end behavior of the following function? x+1/x

A. y approaches positive infinity
B. y approaches -1
C. y approaches 0
D. y approaches 1

Answer 1

The end behavior of the function y = x + 1/x is that y approaches 0 as x approaches infinity, because the 1/x term becomes insignificant compared to the linear x term.

Step-by-step explanation:

The end behavior of the function y = x + 1/x is best described by option C: y approaches 0. As x grows larger in the positive or negative direction, the value of 1/x gets closer and closer to zero. Hence, the function behaves similarly to a linear function y = x, with the slight upward or downward adjustment from the 1/x term becoming insignificant at extreme values of x.

Hence, as x approaches positive or negative infinity, y will approach infinity due to the x term, but due to the 1/x decreasing in impact, it's only the linear x part that dictates the dominant behavior of the function. The end behavior of the function x+1/x can be determined by looking at the highest power of x in the expression. In this case, the highest power of x is 1. As x approaches positive infinity, the value of the function will also approach positive infinity (option A). Therefore, the correct answer is A. y approaches positive infinity.