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 . The least degree the polynomial can have is (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 . The least degree the polynomial can have is (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 $\square$ . The least degree the polynomial can have is $\square$ (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 of a polynomial function
  • A polynomial function graph is continuous and smooth without any breaks, holes, or sharp corners.
  • The given graph is continuous and smooth, so it could be a polynomial function.
Step 2: Identify the real zeros of the polynomial
  • Real zeros of a polynomial are the x-values where the graph intersects the x-axis.
  • From the graph, the polynomial intersects the x-axis at \( x = -2 \) and \( x = 1 \).
Step 3: Determine the least degree the polynomial can have
  • The least degree of a polynomial is determined by the number of turning points plus one.
  • The graph has 2 turning points (one maximum and one minimum), so the least degree is \( 2 + 1 = 3 \).

Final Answer

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