Problem 1 Find a formula for the polynomial of least degree

Problem #1

Find a formula for the polynomial of least degree through the points shown in the graph.
f(x)=__________________

Problem #2

a) What power function does the function above resemble?______________

Problem #3

Problem #4

degree=____________

leading coefficient=_____________

constant coefficient=______________

Problem #5

a) The roots of f(x) are x=_________________

Problem #6

leading coefficient=____________

constant coefficient=______________

Problem #7

a) The roots of f(x) are x=_____________

Problem #8

1) from the graph : zeros: x= -4 , x =1 , x=3

So, polynomial can be written as :f(x) = k(x+4)(x-1)(x-3)

we need to find k coefficient if highest term .As per graph f(x) passes through (-2, 2)

So, 2 = k(-2+4)(-2-1)(-2-3)

2 = k(2)(-3)(-5)

k = 1/15

f(x) = (x+4)(x-1)(x-3)/15

2) y = 3x^3 + 5x^4/(x-6) -9x^5 +8

the highest degree term is -9x^5.o, for very large values of x: y beaves as per highest degree term

So, f(x) = -9x^5 (power function)