Graphs of Polynomials Worksheet
Explore the graphs of polynomial functions, including their end behavior, roots, multiplicity, and turning points.
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Graphs of Polynomials
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Read each question carefully and provide your answer in the space provided. For graphing questions, use the coordinate plane. Show all your work.
1. Which of the following describes the end behavior of the polynomial function f(x) = -2x^3 + 5x - 1?
As x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞
As x → ∞, f(x) → -∞ and as x → -∞, f(x) → ∞
As x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞
As x → ∞, f(x) → -∞ and as x → -∞, f(x) → -∞
2. What is the maximum number of turning points a polynomial of degree 4 can have?
2
3
4
5
3. If a polynomial function has a root with an even multiplicity, its graph will the x-axis at that root.
4. The degree of a polynomial determines its behavior.
5. Describe the relationship between the degree of a polynomial function and the maximum number of x-intercepts it can have.
6. Sketch the graph of the polynomial function f(x) = (x - 1)^2 (x + 2). Label the x-intercepts and describe the end behavior.
7. A polynomial function with an odd degree must have at least one real root.
True
False