Graphing Polynomials Worksheet
Grade 11 worksheet on graphing polynomial functions, including identifying key features and sketching graphs.
Includes
Standards
Topics
Graphing Polynomials
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Read each question carefully and follow the instructions to graph the polynomial functions. Show all your work.
1. Which of the following is NOT a characteristic of a polynomial function's graph?
It is continuous.
It has sharp corners or cusps.
It has smooth, rounded turns.
Its domain is all real numbers.
2. The end behavior of a polynomial function is determined by its term and its .
3. A root with an even multiplicity will cause the graph to the x-axis at that point, while a root with an odd multiplicity will cause the graph to the x-axis.
4. Describe the steps you would take to find the zeros of a polynomial function algebraically.
5. For the polynomial function f(x) = (x + 2)(x - 1)^2:
a) Identify the zeros and their multiplicities.
b) Determine the end behavior of the graph.
c) Find the y-intercept.
d) Sketch the graph of f(x) on the provided coordinate plane.
6. The degree of a polynomial function tells you the maximum number of x-intercepts the graph can have.
True
False
7. Given the graph of a polynomial function, explain how you would determine the possible equation of the function, including its degree, leading coefficient, and approximate zeros.