Graphs of Polynomials
This worksheet focuses on understanding and analyzing 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 answer to the best of your ability. Show all your work where applicable.
1. Which of the following describes the end behavior of the polynomial function f(x) = -2x^4 + 3x^3 - x + 5?
As x → ∞, f(x) → ∞; As x → -∞, f(x) → ∞
As x → ∞, f(x) → -∞; As x → -∞, f(x) → -∞
As x → ∞, f(x) → ∞; As x → -∞, f(x) → -∞
As x → ∞, f(x) → -∞; As x → -∞, f(x) → ∞
2. What is the maximum number of turning points a polynomial of degree 5 can have?
3
4
5
6
3. If a root of a polynomial has a multiplicity of 2, the graph will the x-axis at that point.
4. The is determined by the highest degree term of the polynomial function.
5. Consider the polynomial function P(x) = (x - 1)^2 (x + 2). What are the zeros of the function and their multiplicities? Describe the behavior of the graph at each zero.
6. Sketch a possible graph of a polynomial function that satisfies the following conditions:
- Degree 3
- Leading coefficient is negative
- Zeros at x = -3 (multiplicity 1), x = 0 (multiplicity 1), and x = 2 (multiplicity 1)
7. A polynomial function of odd degree must have at least one real root.
True
False
8. The graph of a polynomial function can have a sharp corner or cusp.
True
False