Question
Describe the end behavior of the function y=x3−x2
.(1 point)
Responses
y→+∞ as x→−∞ and y→+∞ as x→+∞
y→+∞ as x→−∞ and y→+∞ as x→+∞
y→+∞ as x→−∞ and y→−∞ as x→+∞
y→+∞ as x→−∞ and y→−∞ as x→+∞
y→−∞ as x→−∞ and y→+∞ as x→+∞
y→−∞ as x→−∞ and y→+∞ as x→+∞
y→−∞ as x→−∞ and y→−∞ as x→+∞
.(1 point)
Responses
y→+∞ as x→−∞ and y→+∞ as x→+∞
y→+∞ as x→−∞ and y→+∞ as x→+∞
y→+∞ as x→−∞ and y→−∞ as x→+∞
y→+∞ as x→−∞ and y→−∞ as x→+∞
y→−∞ as x→−∞ and y→+∞ as x→+∞
y→−∞ as x→−∞ and y→+∞ as x→+∞
y→−∞ as x→−∞ and y→−∞ as x→+∞
Answers
Answered by
GPT-4o mini
To analyze the end behavior of the function \( y = x^3 - x^2 \), we can consider the dominant term as \( x \) approaches positive and negative infinity.
1. **As \( x \to -\infty \)**:
- The dominant term is \( x^3 \) because it grows faster than \( -x^2 \).
- Therefore, \( y \to -\infty \) as \( x \to -\infty \).
2. **As \( x \to +\infty \)**:
- Again, the dominant term is \( x^3 \).
- Thus, \( y \to +\infty \) as \( x \to +\infty \).
Based on this analysis, the correct description of the end behavior is:
**y→−∞ as x→−∞ and y→+∞ as x→+∞.**
1. **As \( x \to -\infty \)**:
- The dominant term is \( x^3 \) because it grows faster than \( -x^2 \).
- Therefore, \( y \to -\infty \) as \( x \to -\infty \).
2. **As \( x \to +\infty \)**:
- Again, the dominant term is \( x^3 \).
- Thus, \( y \to +\infty \) as \( x \to +\infty \).
Based on this analysis, the correct description of the end behavior is:
**y→−∞ as x→−∞ and y→+∞ as x→+∞.**