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Answer :
To determine the degree of the polynomial function [tex]\( f \)[/tex] given the ordered pairs, we can follow this general method:
1. Understanding Polynomial Degree: The degree of a polynomial is the highest power of [tex]\( x \)[/tex] that appears with a non-zero coefficient.
2. Given Data: Examine the ordered pairs:
- [tex]\((-3, 82)\)[/tex]
- [tex]\((-2, 17)\)[/tex]
- [tex]\((-1, 2)\)[/tex]
- [tex]\( (0, 1)\)[/tex]
- [tex]\( (1, 2)\)[/tex]
- [tex]\( (2, 17)\)[/tex]
- [tex]\( (3, 82)\)[/tex]
3. Symmetrical Values Suggest Even Degree: Notice that [tex]\( f(x) \)[/tex] is symmetrical around the y-axis. For example, [tex]\( f(-3) = 82\)[/tex] and [tex]\( f(3) = 82\)[/tex]. Similarly, [tex]\( f(-2) = 17\)[/tex] and [tex]\( f(2) = 17\)[/tex]. This symmetry suggests the presence of an even degree.
4. Coefficient Pattern: The key step is identifying the degree of this polynomial by calculating or analyzing the coefficients that match such symmetrical values.
5. Result Analysis: Upon examination and calculations, it turns out the highest power of [tex]\( x \)[/tex] that aligns with the given values is 2. Thus, the degree of the polynomial function [tex]\( f \)[/tex] is determined to be 2.
So, the degree of the polynomial [tex]\( f \)[/tex] is 2.
1. Understanding Polynomial Degree: The degree of a polynomial is the highest power of [tex]\( x \)[/tex] that appears with a non-zero coefficient.
2. Given Data: Examine the ordered pairs:
- [tex]\((-3, 82)\)[/tex]
- [tex]\((-2, 17)\)[/tex]
- [tex]\((-1, 2)\)[/tex]
- [tex]\( (0, 1)\)[/tex]
- [tex]\( (1, 2)\)[/tex]
- [tex]\( (2, 17)\)[/tex]
- [tex]\( (3, 82)\)[/tex]
3. Symmetrical Values Suggest Even Degree: Notice that [tex]\( f(x) \)[/tex] is symmetrical around the y-axis. For example, [tex]\( f(-3) = 82\)[/tex] and [tex]\( f(3) = 82\)[/tex]. Similarly, [tex]\( f(-2) = 17\)[/tex] and [tex]\( f(2) = 17\)[/tex]. This symmetry suggests the presence of an even degree.
4. Coefficient Pattern: The key step is identifying the degree of this polynomial by calculating or analyzing the coefficients that match such symmetrical values.
5. Result Analysis: Upon examination and calculations, it turns out the highest power of [tex]\( x \)[/tex] that aligns with the given values is 2. Thus, the degree of the polynomial function [tex]\( f \)[/tex] is determined to be 2.
So, the degree of the polynomial [tex]\( f \)[/tex] is 2.
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