Characteristics of Polynomials
Explore the key characteristics of polynomial functions, including degree, leading coefficient, end behavior, and roots, with this Grade 11 math worksheet.
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Characteristics of Polynomials
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. The of a polynomial is the highest power of the variable in the polynomial.
2. The behavior of the graph of a polynomial function as x approaches positive or negative infinity is called its .
3. A polynomial of degree 2 is called a .
4. The coefficient is the coefficient of the term with the highest degree.
5. Which of the following is NOT a characteristic of a polynomial function?
Smooth and continuous graph
Can have sharp corners or cusps
Domain is all real numbers
Can have multiple x-intercepts
6. What is the degree of the polynomial function f(x) = 3x^4 - 2x^2 + 7x - 1?
1
2
3
4
7. Describe the end behavior of a polynomial function with an odd degree and a positive leading coefficient.
8. How does the multiplicity of a root affect the graph of a polynomial function at that x-intercept?
9. A polynomial function can have a vertical asymptote.
True
False
10. The number of turning points of a polynomial function of degree 'n' is at most n-1.
True
False
11. Analyze the graph of the polynomial function below and determine its key characteristics.
Degree:
Leading Coefficient (positive/negative):
End Behavior:
Number of Real Roots:
x-intercept(s):
y-intercept(s):