Polynomial Review Task for Unit 3 for Algebra 2
I. Explore the graph of the polynomial function
A. Classification
1. Classify this polynomial by degree: ______
2. State the number of terms it has: ______
B. Symmetry
1. Is the function symmetric about the y-axis? ______
2. Is the function symmetric about the origin? ______
3. Is the function even, odd, or neither? ______
C. Domain and Range
1. State the domain of the function: ______
2. State the range of the function: ______
D. X-Intercepts, Factors, and Zeros
1. Identify all the x-intercepts of the graph of the polynomial function: ______
2. Identify all the factors of the polynomial function: ______
3. Identify all the zeros or roots of the polynomial function: ______
4. How many zeros does the function have? ______
E. End-Behaviors
1. Describe the left end-behavior of the graph of this function: ______
2. Describe the right end-behavior of the graph of this function: ______
F. Relative Maximums and Minimums
1. Identify all of the relative minimum(s) in the graph of the polynomial function: ______
2. Identify all of the relative maximum(s) in the graph of the polynomial function: ______
G. Intervals of Increase or Decrease
1. Identify all of the intervals of increase in the graph of the polynomial function: ______
2. Identify all of the intervals of decrease in the graph of the polynomial function: ______
II. Explore the graph of the polynomial function
H. Classification
1. Classify this polynomial by degree: ______
2. State the number of terms it has: ______
I. Symmetry
1. Is the function symmetric about the y-axis? ______
2. Is the function symmetric about the origin? ______
3. Is the function even, odd, or neither? ______
J. Domain and Range
1. State the domain of the function: ______
2. State the range of the function: ______
K. X-Intercepts, Factors, and Zeros
1. Identify all the x-intercepts of the graph of the polynomial function: ______
2. Identify all the factors of the polynomial function: ______
3. Identify all the zeros or roots of the polynomial function: ______
4. How many zeros does the function have? ______
L. End-Behaviors
1. Describe the left end-behavior of the graph of this function: ______
2. Describe the right end-behavior of the graph of this function: ______
M. Relative Maximums and Minimums
1. Identify all of the relative minimum(s) in the graph of the polynomial function: ______
2. Identify all of the relative maximum(s) in the graph of the polynomial function: ______
N. Intervals of Increase or Decrease
1. Identify all of the intervals of increase in the graph of the polynomial function: ______
2. Identify all of the intervals of decrease in the graph of the polynomial function: ______
III. Problem Solving and Applications
A. From 1985 to 1995, the number of nursing schools in the United States could be modeled by
where f(t) is the number of graduates, in thousands, and t is the number of years since 1985.
1. Describe the right end-behavior of the graph of this function: ______
2. Would you expect the number of nursing graduates in 2010 to be more or less than in 1995? Why?
______
3. Find the first year when the number of nursing graduates is over 90,000. ______
B. The producer price index of butter from 1991 to 1999 can be modeled by the function where x is the number of years since 1991
1. Identify any turning points on the graph in the interval . ______
2. What real-life meaning do these points have? ______
______
C. Construct a polynomial having the following characteristics: third degree, negative leading coefficient, and three real zeros. Sketch the graph of your polynomial below and label the x-intercepts and all turning points on the graph.