Question

Describe the end behavior of the function y=logx .(1 point) Responses As x→0+ , y→∞ , and as x→∞ , y→−∞ . As x right arrow 0 superscript positive baseline , y right arrow infinity , and as x right arrow infinity , y right arrow negative inifinity . As x→−∞ , y→−∞ , and as x→0 , y→∞ . As x right arrow negative infinity , y right arrow negative inifinity , and as x right arrow 0 , y right arrow infinity . As x→−∞ , y→−∞ , and as x→∞ , y→∞ . As x right arrow negative infinity , y right arrow negative infinity , and as x right arrow infinity , y right arrow infinity . As x→0+ , y→−∞ , and as x→∞ , y→∞ . As x right arrow 0 superscript positive baseline , y right arrow negative inifinity , and as x right arrow inifinity , y right arrow infinity .

Answer 1

To analyze the end behavior of the function \( y = \log x \), we should consider the values of \( y \) as \( x \) approaches \( 0 \) from the right (denoted as \( x \to 0^+ \)) and as \( x \) approaches infinity (denoted as \( x \to \infty \)).

1. As \( x \to 0^+ \):
- The logarithm function approaches negative infinity. Therefore, \( y \to -\infty \).

2. As \( x \to \infty \):
- The logarithm function increases without bound. Therefore, \( y \to \infty \).

Based on this analysis, the correct description of the end behavior of the function is:

- As \( x \to 0^+ \), \( y \to -\infty \).
- As \( x \to \infty \), \( y \to \infty \).

None of the provided options perfectly match this description, but the closest option that correctly represents the behavior as \( x \to 0^+ \) is:

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