Algebra 2 Worksheet
AII.7f – End Behavior
Name:_____________________________
Determine the end behavior for each function below. Place the letter(s) of the appropriate
statement(s) on the line provided.
A. As x approaches ∞, y approaches ∞
B. As x approaches -∞, y approaches ∞
C. As x approaches ∞, y approaches -∞
D. As x approaches -∞, y approaches -∞
1. __________
2. __________
3. __________
Give the end behavior for each function by filling in each blank.
4. As x approaches ____, y approaches ____
5. As x approaches ____, y approaches ____
As x approaches ____, y approaches ____
As x approaches ____, y approaches ____
Give the end behavior for each function.
6.
7.
8.
9. 𝑦 = −3𝑥 + 7
10. 𝑦 = 𝑥
1
1
11. 𝑦 = 100 (𝑥 − 5)2 (𝑥 + 6)2
12. Sketch the graph of 𝑦 = √𝑥 + 5 + 2. What is the end behavior of this function? Explain your
answer.
Sketch a graph that has the given end behavior.
13. As x approaches -∞, y approaches ∞
As x approaches ∞, y approaches ∞
14. As x approaches -∞, y approaches -∞
As x approaches ∞, y approaches 0
Extension:
A. For each function in #1 – 12, give the name and equation of the parent function.
Function Name
Parent Equation
Function Name
Parent Equation
1) ________________ ______________
7) ________________ ______________
2) ________________ ______________
8) ________________ ______________
3) ________________ ______________
9) ________________ ______________
4) ________________ ______________
10) ________________ ______________
5) ________________ ______________
11) ________________ ______________
6) ________________ ______________
12) ________________ ______________
B. Which of our parent functions could have transformations with the following end behavior?
Explain your answer.
Left End Behavior: As x approaches -∞, y approaches ∞
Right End Behavior: As x approaches ∞, y approaches -∞