Unit 6 Pre-assessment [PDF]

Unit 6 Pre-assessment Form a polynomial based on the zeros below. 1. 2. 3. 4.

Zeros: -2, -4 with a multiplicity of 2, 2 Zeros: 0 with a multiplicity of 3, 3, 5 with a multiplicity of 2 Zeros: -3, 4, 3 – 2i Zeros: 2, 4i, -2 – 3i

Find a polynomial or rational function that might have the given graph below. 5.

6.

7.

8.

Graph each polynomial or rational function below. 9. 𝑓(𝑥) = (𝑥 − 2)(𝑥 + 4)(𝑥 − 5) 10. 𝑔(𝑥) = 𝑥 − 13𝑥 + 36 11. ℎ(𝑥) = −2𝑥 − 12𝑥 − 18𝑥 12. 𝑓 (𝑥 )

=

13. 𝑔 (𝑥 )

=

( (

) )(

)

14. ℎ(𝑥 ) =

Answer each question below based on the given graph. 15. What is the function’s domain? 16. What is the function’s range? 17. Where is the function increasing? 18. Where is the function decreasing? 19. List all local minimums. 20. List all local maximums. 21. Where is f(x) > 0? 22. Where is f(x) < 0? 23. Where is f(x) = 10?

24. What is the function’s domain? 25. What is the function’s range? 26. Where is the function increasing? 27. Where is the function decreasing? 28. Where is f(x) > 0? 29. Where is f(x) < 0? 30. Where is f(x) = 5?

Find all the zeros of the polynomial functions below. Write your final answer in factored form. Remember to use all your tools! 31. 𝑓(𝑥) = 3𝑥 + 15𝑥 + 12 32. 𝑔(𝑥) = 2𝑥 + 2𝑥 − 11𝑥 + 𝑥 − 6 33. ℎ(𝑥) = 2𝑥 + 7𝑥 − 5𝑥 − 28𝑥 − 12 34. 𝑝(𝑥) = 4𝑥 − 4𝑥 − 7𝑥 − 2 35. 𝑚(𝑥) = 𝑥 + 6𝑥 + 11𝑥 + 12𝑥 + 18

Answer Key 1. 𝑓(𝑥) = (𝑥 + 2)(𝑥 + 4) (𝑥 − 2) = 𝑥 + 8𝑥 + 12𝑥 − 32𝑥 − 64 2. 𝑓(𝑥) = 𝑥 (𝑥 − 3)(𝑥 − 5) = 𝑥 − 13𝑥 + 55𝑥 − 75𝑥 3. 𝑓(𝑥) = (𝑥 + 3)(𝑥 − 4) 𝑥 − (3 − 2𝑖) 𝑥 − (3 + 2𝑖) = 𝑥 − 7𝑥 + 7𝑥 + 59𝑥 − 156 4. 𝑓(𝑥) = (𝑥 − 2)(𝑥 − 4𝑖)(𝑥 + 4𝑖) 𝑥 − (−2 − 3𝑖) 𝑥 − (−2 + 3𝑖) = 𝑥 + 25𝑥 − 26𝑥 + 144𝑥 − 416 5. 𝑓(𝑥) = (𝑥 + 4)(𝑥 − 2) 6. 𝑓(𝑥) = 𝑥 (𝑥 − 3)(𝑥 + 3) ( )( ) 7. 𝑓 (𝑥 ) = ( )( ) ( )( ) 8. 𝑓 (𝑥 ) = ( )( )

9.

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14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

(-∞, ∞) (-∞, ∞) (-∞, -3), (-1,5, 0), (2.2, ∞) (-3, -1.5), (0, 2.2) -24 at x = -1.5, -106 at x = 2.2 0 at x = -3, 0 at x = 0 (3, ∞) (-∞, 3] X = 3, 1 (-∞, ∞) x ≠ -5, 3 (-∞, -3), [-1.1, ∞) (-2, 3), (3, ∞) (-∞, -5), (-5, -2) (-5, 4), (1, 3) (-∞, -5), [-4, 1], (3, ∞)

30. X = 2.2, -4.7 31. 𝑓(𝑥) = (3𝑥 + 3)(𝑥 + 4) 32. 𝑓(𝑥) = (𝑥 − 2)(𝑥 + 3)(2𝑥 + 1) 33. 𝑓(𝑥) = (𝑥 + 3)(𝑥 + 2)(𝑥 + )(𝑥 − 2) 34. 𝑓(𝑥) = (𝑥 − 2)(2𝑥 + 1) 35. 𝑓(𝑥) = (𝑥 + 3) (𝑥 + √2𝑖)(𝑥 − √2𝑖)