Question

Which statement best describes left-sided behavior and right-sided behavior of the function as x → 0?

A. The left-sided behavior approaches a finite value, and the right-sided behavior approaches positive infinity.

B. The left-sided behavior approaches positive infinity, and the right-sided behavior approaches a finite value.

C. The left-sided behavior approaches negative infinity, and the right-sided behavior approaches positive infinity.

D. The left-sided behavior approaches a finite value, and the right-sided behavior approaches negative infinity.

Answer 1

The left-sided behavior of the function as x approaches 0 is negative infinity, and the right-sided behavior is positive infinity.

Step-by-step explanation:

The left-sided behavior of the function as x approaches 0 can be determined by evaluating the function from the left side of 0. In this case, when x approaches 0 from the left side (x < 0), the function y = 1/x approaches negative infinity (-∞). This is because as x gets closer and closer to 0 from the left side, the denominator (x) becomes smaller and smaller, causing the value of the function to decrease without bound.

On the other hand, the right-sided behavior of the function as x approaches 0 can be determined by evaluating the function from the right side of 0. In this case, when x approaches 0 from the right side (x > 0), the function y = 1/x approaches positive infinity (+∞). This is because as x gets closer and closer to 0 from the right side, the denominator (x) becomes smaller and smaller, causing the value of the function to increase without bound.

Therefore, the statement that best describes the left-sided behavior and right-sided behavior of the function as x approaches 0 is:

C. The left-sided behavior approaches negative infinity, and the right-sided behavior approaches positive infinity.