Sketching Multiplicities Solutions

• To sketch roots, you need:

  • the polynomial    equation   

         or

• • 
the    roots     and    multiplicities    .


• The steps for sketching multiplicities include:


1. 1. Perform the    leading coefficient test     (estimate a, n).

   2. Sketch the    end behavior   .

   3. Plot the    roots    on the x-axis.

   4. Connect the end behavior to the roots using the    multiplicities    (CBS).


• Remember, a sketch does not demonstrate the    exact scale    of a graph. A sketch gives a general picture of what is happening at key points.

Example 3

Sketch the roots. Name the degree.

Example 4

Sketch the zeros of the function.

$$\begin{gathered} x^2{\left(x–2.5\right)}^3\left(x+2\right)\left(x–5\right)=0 \\ \mathrm{B} \mathrm{S} \mathrm{C} \mathrm{C} \end{gathered}$$