3/13/2023 0 Comments Polynomial graph![]() Increases without bound and will either rise or fall as x xĭecreases without bound. Will either ultimately rise or fall as x x + a 1 x + a 0 f ( x ) = a n x n + a n − 1 x n − 1 +. ![]() See Figure 8 for examples of graphs of polynomial functions with multiplicity 1, 2, and 3.į ( x ) = a n x n + a n − 1 x n − 1 +. For zeros with odd multiplicities, the graphs cross or intersect the x-axis. We call this a triple zero, or a zero with multiplicity 3.įor zeros with even multiplicities, the graphs touch or are tangent to the x-axis. This factor is cubic (degree 3), so the behavior near the intercept is like that of a cubic-with the same S-shape near the intercept as the toolkit function f ( x ) = x 3. The graph passes through the axis at the intercept, but flattens out a bit first. The x-intercept x = − 1 x = − 1 is the repeated solution of factor ( x + 1 ) 3 = 0. The zero associated with this factor, x = 2, x = 2, has multiplicity 2 because the factor ( x − 2 ) ( x − 2 ) occurs twice. The number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity. The factor is repeated, that is, the factor ( x − 2 ) ( x − 2 ) appears twice.
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