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Graph using your knowlege of end behavior, zeros, and bounce/pass. 

 Apr 19, 2020
 #1
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3)  f(x)  =  -2x2(x - 2)3(x + 4)4(x - 5)

 

To find the degree:  x2 has degree 2

                                (x - 2)3 has degree 3

                                (x + 4)4 has degree 4

                                (x - 5) has degree 1

    adding the degrees together, we get degree 10

 

To find the end behavior:

  right-end: put a large positive number in for each variable

                     -4:  negative

                   x2  is positive

                   (x - 2)3  is positive

                   (x + 4)4  is positive

                   (x - 5)  is positive

         multiplying these together:  negative   --->  right-end goes downward

  left-end: 

put a large negative number in for each variable

                     -4:  negative

                   x2  is positive

                   (x - 2)3  is negative

                   (x + 4)4  is positive

                   (x - 5)  is negative

         multiplying these together:  negative   --->  left-end goes downward

 

Zeros:  bounces if the exponent is positive; passes through if the exponent is negative

      x2 :  bounces at 0

     (x - 2)3 : passes through at 2

     (x + 4)4 : bounces at -4

     (x - 5) : passes through at 5

 

4)  f(x)  =  3x7 - 48x5

            =  3x5(x2 - 16) 

            =  3x5(x + 4)(x - 4)

 

and now do the same type of analysis as done in problem 3).

 Apr 20, 2020

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