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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 -∞