Question

Describe the end behavior of the function y=logx.
A. As x→−∞,y→−∞, and as x→0,y→∞.
B. As x→0
+
,y→−∞, and as x→∞,y→∞.
C. As x→0
+
,y→∞, and as x→∞,y→−∞.
D. As x→−∞,y→−∞, and as x→∞,y→∞.

Answer 1

To analyze the end behavior of the function \( y = \log x \), we need to examine what happens to \( y \) as \( x \) approaches 0 from the right ( \( x \to 0^+ \) ) and as \( x \) approaches infinity ( \( x \to \infty \) ).

1. **As \( x \to 0^+ \)**: The logarithm of a number close to zero from the positive side approaches negative infinity. Thus, \( y \to -\infty \).

2. **As \( x \to \infty \)**: The logarithm of a very large number increases without bound. Therefore, \( y \to \infty \).

Given these observations, we can summarize:
- As \( x \to 0^+ \), \( y \to -\infty \)
- As \( x \to \infty \), \( y \to \infty \)

Based on the provided choices, the correct answer is:

**B. As \( x \to 0^+ \), \( y \to -\infty \), and as \( x \to \infty \), \( y \to \infty \).**