Graphs of Polynomials Worksheet
Explore and analyze the graphs of polynomial functions, identifying key features such as end behavior, roots, 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 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) → ∞ 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 real roots a polynomial of degree 3 can have?
1
2
3
4
3. The graph of a polynomial function with an odd degree and a positive leading coefficient will typically have end behavior where as x → -∞, f(x) → and as x → ∞, f(x) → .
4. A polynomial function of degree 'n' can have at most turning points.
5. Describe the relationship between the multiplicity of a root and the behavior of the graph at that x-intercept. Provide an example.
6. Sketch the graph of a polynomial function that satisfies the following conditions:
- Degree 3
- Roots at x = -2 (multiplicity 1), x = 1 (multiplicity 2)
- Leading coefficient is positive
7. The graph of every polynomial function has at least one x-intercept.
True
False
8. A polynomial function can have more x-intercepts than its degree.
True
False