Questions: Determine whether the graph could be the graph of a polynomial function. If it could be, list the real zeros and state the least degree the polynomial can have. Select the correct choice below and fill in any answer boxes within your choice. A. The graph shows a polynomial function. The real zero(s) is/are -2, 1, 3. The least degree the polynomial can have is 4. (Use a comma to separate answers as needed. Round to the nearest integer as needed.) B. The graph does not show a polynomial function.

Determine whether the graph could be the graph of a polynomial function. If it could be, list the real zeros and state the least degree the polynomial can have. Select the correct choice below and fill in any answer boxes within your choice. A. The graph shows a polynomial function. The real zero(s) is/are -2, 1, 3. The least degree the polynomial can have is 4. (Use a comma to separate answers as needed. Round to the nearest integer as needed.) B. The graph does not show a polynomial function.
Transcript text: Determine whether the graph could be the graph of a polynomial function If it could be, list the real zeros and state the least degree the polynomial can have. Select the correct choice below and fill in any answer boxes within your choice. A. The graph shows a polynomial function. The real zero(s) is/are $-2,1,3$. The least degree the polynomial can have is 4 . (Use a comma to separate answers as needed. Round to the nearest integer as needed.) B. The graph does not show a polynomial function.
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Solution

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Solution Steps

Step 1: Determine if the graph could be a polynomial function
  • A polynomial function is a continuous curve that can have multiple turning points and crosses the x-axis at its real zeros.
  • The given graph shows a continuous curve with turning points and crosses the x-axis at three points.
Step 2: Identify the real zeros
  • The graph crosses the x-axis at three points, which are the real zeros of the polynomial.
  • From the graph, the real zeros are approximately -2, 1, and 3.
Step 3: Determine the least degree of the polynomial
  • The least degree of a polynomial is determined by the number of turning points plus one.
  • The graph has three turning points, so the least degree of the polynomial is 3 + 1 = 4.

Final Answer

  • The graph shows a polynomial function.
  • The real zeros are -2, 1, and 3.
  • The least degree the polynomial can have is 4.
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