Give an example of 2 different possible polynomial functions
Give an example of 2 different possible polynomial functions whose graph is shown below:
Solution
root at x = -1 ( multplicity 2 as it touches the graph)
x = 1 ;
root at x = 2 ( multplicity 2 as it touches the graph)
Its an odd polynomial with degree =5 ; ends in opposite direction.
f(x) ---> inf +ve ; x .---> -inf
f(x) ---> inf -ve ; x .---> +inf
highest polynomial -ve
f(x) = a(x +1)^2(x -1)(x -2)^2
y interept : ( 0, 4)
4 = a(1)(-1)(2)^2 ; a = -1
f(x) = -(x+1)^2(x -1)(x -2)^2
