Polynomial Functions Test

1. Given a function of the form y = a[k(x– d)]ⁿ+ c, where k > 0, the transformation that occurs by changing the value of k is

2. The graph of the function y= x⁴ is transformed to the graph of the function y = –2(x – 3)⁴ + 1 by

3. The graph of the function y = x(x– 1)³(x+ 2)² would most closely resemble

4. Which of the following graphs represents the function  y = 2x⁵ – 3x⁴+ 1?

5. The least possible degree of the polynomial function represented by the graph shown is 

6. An equation representing a function that extends from quadrant 2 to quadrant 4 is

7. Which of the following is not a polynomial function?

8. Given the function y= (x – 1)²(x + 1)², which finite differences will be equal (or constant)?

9. An equation for a cubic function with zeros 1, –2, and 3 that passes through the point (2, 12) is

10. An equation for the graph shown is

11. Given the function y = –3x² – 5x+ 1, the second differences will all equal

12. Which of the following is an even function?

13. The number of times that the function y= (x – 1)³ (x+ 2) (x– 4)² changes sign is

14. The function y = (x – 4)²(x – 7)(x + 3)³ is negative on the intervals

15. The number of people, P, at a playground after tmin is given by P = t³+ 4t + 20. The average rate of change of the number of people at the playground from 3 min to 4 min is

16. The number of people, P, at a playground after t min is given by P = t³+ 4t + 20. The instantaneous rate of change of the number of people at the playground after 1 min is approximately

17. Fill in the blank with the correct word.

18. Match the items in the box with each criterion below by dragging.

19. Fill in the blank with the correct word.

20. Odd-degree polynomials have at least one x-intercept.

21. Determine an equation for the quartic polynomial function represented by the table of values.

22. An equation for a quintic function with zeros 1, 0, and 2 that passes through the point (–1, 24) is

23. Determine algebraically whether the function is even, odd, or neither.  

\(\: g(x) = -2\left(4+x \right)\left(4-x \right)\left(x+5 \right)\left(5-x\right) \)

24. A point P(a, b)  transforms into Q(-3, 13)  while y = f(x)  transforms into y = -2f(-3x + 4) + 5. State the mapping rule and find the values of a and b.