Finding Polynomial Functions from Graphs
This worksheet helps Grade 11 students practice identifying key features of polynomial graphs and using them to construct polynomial functions.
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Standards
Finding Polynomial Functions from Graphs
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Carefully analyze each graph of a polynomial function. Identify the zeros, their multiplicities, and the end behavior. Use this information to write a possible equation for the polynomial function in factored form. Assume the leading coefficient is 1 unless otherwise specified.
1. Analyze the graph below and write a possible polynomial function in factored form.
Zeros and Multiplicities:
End Behavior:
Possible Function f(x) =
2. Which of the following polynomial functions could represent the graph shown?
f(x) = (x+2)(x-1)(x-3)
f(x) = -(x+2)(x-1)(x-3)
f(x) = (x+2)^2(x-1)(x-3)
f(x) = (x-2)(x+1)(x+3)
3. If a polynomial graph touches the x-axis at a zero and turns around, the multiplicity of that zero is .
4. If a polynomial graph crosses the x-axis at a zero, the multiplicity of that zero is .
5. For a polynomial with an odd degree and a positive leading coefficient, the end behavior is as x → -∞, f(x) → and as x → +∞, f(x) → .
6. A polynomial function of degree 'n' can have at most 'n' real zeros.
True
False
7. Consider a polynomial graph that goes down on the left and up on the right. What can you conclude about its degree and leading coefficient?
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