End Behavior
Left end behavior describes the movement of the graph when x is very, very small.
Verbally: As x approaches −∞ , f ( x ) ………………
Right end behavior describes the movement of the graph when x is very, very large
Verbally: As x approaches +∞ , f ( x ) ………………
Practice - End behavior can be a little tricky. You must practice!
1. Quadratic Function
Think graph:
Left:
Think
x → −∞, f ( x ) → ____
Verbally: As x approaches −∞ ,
Right
Think
f ( x)
______________without bound
x → +∞, f ( x ) → ____
Verbally: As x approaches +∞ ,
f ( x)
______________without bound
2. What other parent function has the same end behavior?
3. Cubic Function
Left:
Think
Think graph:
x → −∞, f ( x ) → ____
Verbally: As x approaches −∞ ,
Right
Think
f ( x)
______________without ____________.
x → +∞, f ( x ) → ____
Verbally: As x approaches +∞ ,
f ( x)
______________without ___________.
4. What other parent function has the same end behavior?
5. Reciprocal Function
Left:
Think
Think graph:
x → −∞, f ( x ) → ____
Verbally: As x approaches −∞ ,
Right
Think
f ( x)
__________________________
x → +∞, f ( x ) → ____
Verbally: As x approaches +∞ ,
f ( x)
_________________________
6. Constant Function
Left:
Think
Think graph:
x → −∞, f ( x ) → ____
Verbally: As x approaches −∞ ,
Right
Think
7. Square Root Function
Think
Think
8. Exponential Function
Think
Think
9. Logarithmic Function
Think
Think
__________________________
f ( x)
_________________________
Think graph:
f ( x)
__________________________
f ( x)
_________________________
Think graph:
x → −∞, f ( x ) → ____
Verbally: As x approaches −∞ ,
Right
f ( x)
x → +∞, f ( x ) → ____
Verbally: As x approaches +∞ ,
Left:
Think graph:
x → −∞, f ( x ) → ____
Verbally: As x approaches −∞ ,
Right
_________________________
x → +∞, f ( x ) → ____
Verbally: As x approaches +∞ ,
Left:
f ( x)
x → −∞, f ( x ) → ____
Verbally: As x approaches −∞ ,
Right
__________________________
x → +∞, f ( x ) → ____
Verbally: As x approaches +∞ ,
Left:
f ( x)
f ( x)
__________________________
x → +∞, f ( x ) → ____
Verbally: As x approaches +∞ ,
f ( x)
_________________________