End Behavior of Polynomials Worksheet
Explore the end behavior of polynomial functions based on their degree and leading coefficient with this Grade 12 math worksheet.
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End Behavior of Polynomials
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Carefully read each question and determine the end behavior of the given polynomial functions. Indicate whether the function rises or falls to the left and to the right.
1. What is the end behavior of the polynomial function f(x) = -3x^4 + 2x^3 - 5x + 1?
Rises left, Rises right
Rises left, Falls right
Falls left, Rises right
Falls left, Falls right
2. Which of the following functions has the same end behavior as g(x) = x^3 + 2x - 7?
h(x) = -x^3 + 4x^2
k(x) = x^4 - 3x^2 + 1
p(x) = 2x^3 - x + 5
q(x) = -x^4 + 6x
3. If a polynomial function has an even degree and a positive leading coefficient, its end behavior is that it to the left and to the right.
4. For a polynomial function with an odd degree and a negative leading coefficient, it to the left and to the right.
5. The end behavior of a polynomial function is determined by its constant term.
True
False
6. A polynomial function with an even degree and a negative leading coefficient will have both ends of its graph pointing downwards.
True
False
7. Describe the end behavior of the polynomial function P(x) = -x^5 + 3x^4 - 2x^2 + 8.
8. Consider a polynomial function with an odd degree and a positive leading coefficient. If you were to sketch its graph, what would its end behavior look like?