Polynomial Functions And Their Graphs

About the book author. The sum of the multiplicities must be 6.

Polynomial Functions And Their Graphs Seeking Help For A Deeper

Polynomial functions also display graphs that have no breaks.

Polynomial functions and their graphs. The next zero occurs at the graph looks almost linear at this point. Another characteristic of the graph of a polynomial function is where it intersects the x axis. The zero of has multiplicity.

The only real information that we re going to need is a complete list of all the zeroes including multiplicity for the polynomial. In this unit we will use everything that we know about polynomials in order to analyze their graphical behavior. Specifically we will find polynomials zeros i e x intercepts and analyze how they behave as the x values become infinitely positive or infinitely negative i e end behavior.

Recall that these types of graphs are called smooth curves. Polynomial functions of degree 2 or more have graphs that do not have sharp corners. The next zero occurs at x 1 x 1.

For any polynomial if the root has an odd multiplicity at root c the graph of the function crosses the x axis at x c. The graph touches the x axis so the multiplicity of the zero must be even. The polynomial function is of degree n which is 6.

In this section we are going to look at a method for getting a rough sketch of a general polynomial. The polynomial function is of degree the sum of the multiplicities must be. Curves with no breaks are called continuous.

If the root has an even multiplicity at root c the graph meets but doesn t cross the x axis at x c. Starting from the left the first zero occurs at the graph touches the x axis so the multiplicity of the zero must be even. The zero of 3 has multiplicity 2.

Starting from the left the first zero occurs at x 3 x 3. To determine where a function f intersects the x axis we need to solve the equation f x 0 for n the case of the linear function f x mx b the x intercept is given by solving the equation mx b 0. Zeros of polynomial functions.

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