Question
Describe the end behavior of the function y=lnx .(1 point) Responses As x → 0+, y →∞ and as x →∞, y →−∞ . As x → 0+, y →∞ and as x →∞, y →−∞ . As x → 0+, y →−∞ and as x →∞, y →∞ . As x → 0+, y →−∞ and as x →∞, y →∞ . As x →−∞, y →−∞ and as x → 0, y →∞ . As x →−∞, y →−∞ and as x → 0, y →∞ . As x →−∞, y →−∞ and as x →∞, y →∞ .
Answers
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GPT-4o mini
To analyze the end behavior of the function \( y = \ln x \):
1. **As \( x \to 0^+ \)**: The natural logarithm \( \ln x \) approaches negative infinity. Therefore, \( y \to -\infty \).
2. **As \( x \to \infty \)**: The natural logarithm \( \ln x \) approaches positive infinity. Thus, \( y \to \infty \).
Putting it all together, we have:
- As \( x \to 0^+ \), \( y \to -\infty \).
- As \( x \to \infty \), \( y \to \infty \).
The correct response that matches this analysis is:
**As \( x \to 0^+, y \to -\infty \) and as \( x \to \infty, y \to \infty \).**
1. **As \( x \to 0^+ \)**: The natural logarithm \( \ln x \) approaches negative infinity. Therefore, \( y \to -\infty \).
2. **As \( x \to \infty \)**: The natural logarithm \( \ln x \) approaches positive infinity. Thus, \( y \to \infty \).
Putting it all together, we have:
- As \( x \to 0^+ \), \( y \to -\infty \).
- As \( x \to \infty \), \( y \to \infty \).
The correct response that matches this analysis is:
**As \( x \to 0^+, y \to -\infty \) and as \( x \to \infty, y \to \infty \).**