text: Example OAF.PFF.3 : $P(x) =\frac 1 2*(x^2+1)*(x-2)*(x+1)$.
  Notice: $A=\frac 1 2, r_1=2$ , and $r_2= -1$ and $g_P(x)=x^2 + 1$.
  Draw a mapping diagram and graph of $P$ yourself or explore the GeoGebra figure.
  
  Given a point / number, $x$, on the source line, there is a unique arrow  meeting the target line at the point / number, $P(x) =\frac 1 2*(x^2+1)*(x-2)*(x+1)$., which corresponds to the polynomial function's value for $x$.
  
  When the point in the domain is $0$, the arrow points to $f(0) = \frac 1 2 *(1)*(-2)*(1) = -1$  visualizing the "Y-intercept" on the graph of $P$.
  The X- intercepts are the values for $a$ on the domain axis from which the arrow hits the number $0$  on the target. For this function, those values is $a=2$ and $a=-1$, the values of the real roots, $r_1$ and $r_2$.
explanation: The text extract provides a detailed explanation of a polynomial function \( P(x) = \frac{1}{2} (x^2 + 1) (x - 2) (x + 1) \). It includes the coefficients and roots of the polynomial, and describes how to draw a mapping diagram and graph of the function. The extract also explains the Y-intercept and X-intercepts of the function.
  
  The text does not contain a specific question or a question-and-answer pair. It is primarily an instructional or explanatory text.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Example OAF.PFF.3 : $P(x) =\frac 1 2*(x^2+1)*(x-2)*(x+1)$.
  Notice: $A=\frac 1 2, r_1=2$ , and $r_2= -1$ and $g_P(x)=x^2 + 1$.
  Draw a mapping diagram and graph of $P$ yourself or explore the GeoGebra figure.
  
  Given a point / number, $x$, on the source line, there is a unique arrow  meeting the target line at the point / number, $P(x) =\frac 1 2*(x^2+1)*(x-2)*(x+1)$., which corresponds to the polynomial function's value for $x$.
  
  When the point in the domain is $0$, the arrow points to $f(0) = \frac 1 2 *(1)*(-2)*(1) = -1$  visualizing the "Y-intercept" on the graph of $P$.
  The X- intercepts are the values for $a$ on the domain axis from which the arrow hits the number $0$  on the target. For this function, those values is $a=2$ and $a=-1$, the values of the real roots, $r_1$ and $r_2$.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text extract provides a detailed explanation of a polynomial function \( P(x) = \frac{1}{2} (x^2 + 1) (x - 2) (x + 1) \). It includes the coefficients and roots of the polynomial, and describes how to draw a mapping diagram and graph of the function. The extract also explains the Y-intercept and X-intercepts of the function.
  
  The text does not contain a specific question or a question-and-answer pair. It is primarily an instructional or explanatory text.
  
  Label: no-question