A polynomial function can be graphed by determining the defining
characteristics of the graph of the function.
The option that is true about graphing polynomial function is C. The real zeros that are found using synthetic division and the division algorithm are x-intercepts of the graph of the polynomial function.
Reason:
The steps Graphing polynomial functions includes;
- Finding the intercepts of the graphs.
- Determining if the polynomial has symmetry.
- Expressing the x-intercepts of the polynomial based on the multiplicities of the zeros.
- Analysis of the leading term to determine the graph's end behavior.
- Sketching the graph with the above information of x-intercepts, and end behavior.
From the given options, we have;
- The factor theorem is used to find a polynomial's roots (zeros) and to factor a polynomial. Therefore, the factor theorem does not determine the end behavior, and therefore, the general shape of the polynomial function
- The rational zeros theorem gives the form of the rational zeros of a polynomial. Therefore, the rational zeros theorem does not determine the non rational zeros of the polynomial or the graph's
- The remainder theorem specifies that factors of a polynomial gives the zeros of the polynomial, the factor theorem is the reverse of the remainder theorem. It does not determine the end behavior
The zeros of the polynomial gives the x-intercept of the polynomial
Therefore, the option;
- The real zeros that are found using synthetic division and the division algorithm are x-intercepts of the graph of the polynomial function, is true
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