End Behavior Calculator
End Behavior Analysis
Function Type:
As x → ∞:
As x → -∞:
What is End Behavior?
End behavior describes how a function behaves as x approaches positive or negative infinity. Understanding end behavior helps predict function values for very large or small inputs.
Types of Functions
Polynomial Functions
End behavior depends on:
- Degree of the polynomial
- Sign of leading coefficient
- Whether degree is even or odd
Rational Functions
End behavior depends on:
- Degrees of numerator and denominator
- Leading coefficients of both parts
- Relationship between degrees
Understanding Results
- ↑: Function increases without bound
- ↓: Function decreases without bound
- →: Function approaches a value
- HA: Horizontal asymptote
Common End Behaviors
- Even degree, positive leading coefficient: Both ends up
- Even degree, negative leading coefficient: Both ends down
- Odd degree, positive leading coefficient: Left down, right up
- Odd degree, negative leading coefficient: Left up, right down
Frequently Asked Questions
Why is end behavior important?
End behavior helps understand function trends, predict values, and identify asymptotes, which is crucial for graphing and analyzing functions.
How do I determine end behavior?
Look at the highest degree terms and their coefficients. For rational functions, compare degrees of numerator and denominator.
What are asymptotes?
Asymptotes are values that a function approaches but never reaches. They help describe function behavior at extreme values.