Question

3.1.77 Which of the following is a polynomial function that might have the given graph! Construct a polynomial function that might have In the graph below, the coordinates of the indicated point are 1. the given graph (Use the smallest degree posible) OBO OA ---236x – 23 – 47 1-5 = 23x - 2yx = 45 OC ***+2xx-276-4 -2)(x-2)(x-4 *+234-28 - 4 O ***+23-262-4) OD.) OE

Answer 1

When graph touched x axis and bounce back then multiplicity of zero is even when it crosses then odd

At -2,4 graph crosses x axis so multiplicity odd

At 2 multiplicity even

f(x)=a (x+2)(x-2)^2(x-4)

Now at x=1,f(x)=-9/8

so a= 1/8

f(x)=(1/8)(x+2)(x-2)^2(x-4)

Option c is right

Answer 2

In the graph below, the coordinates of the indicated point are

1,4516.

Construct a polynomial function that might have the given graph. (Use the smallest degree possible.)