SOLUTION: I am sorry I know this is a lengthy question but I am just not sure what the answers are. f(x)=1/4x^3+4x2-x i. What are the end behaviours of this type of function (what qua

Question 1119974: I am sorry I know this is a lengthy question but I am just not sure what the answers are.
f(x)=1/4x^3+4x2-x
i. What are the end behaviours of this type of function (what quadrant does it begin and end in?)
ii. What is the maximum and minimum number of�x-intercepts for this type of function?
iii. What is the maximum and minimum number of turns for this type of function?
iv. State if there are any restrictions on the domain and range on this type of function.
Any help to any of these questions would be so helpful thank you so much in advance.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It is a cubic so x at -oo it is -oo and x at + oo is +oo. The only term that matters at end behavior is the term with the largest exponent.
The number of sign changes are 1, so it can have one positive root.
Change the signs and it is -(1/4)x^3+4x^2+x. It can have one negative root.
The third root must be 0.
This means 2 turns.
There are no restrictions on either the domain or range of the function, since one is not dividing by 0 anywhere.
--near 0

RELATED QUESTIONS
I am sorry I know this is a lengthy question but I am just not sure what the answers are. (answered by solver91311)

I am sorry I know this is a lengthy question but I am just not sure what the answers are. (answered by solver91311)

i am asked to solve 12x^2+7x=10. i think th answers are x=-5/4 and 2/3. i am just... (answered by checkley77)

I am just learning to do functions, domain. When f(x)=x+1 and g(x)=2x find: a)... (answered by stanbon)

3 square root sign 64x7 divided by 3 square root sign 4x I have asked this question... (answered by Earlsdon)

{{{ log( 3,x ) }}} ^2 + {{{ log( 3,x^2) }}} -3 = 0 What is x? Basically, this question (answered by josgarithmetic)

i need a little help to make sure i am doing this right. Solve: 2x-5=(the square root... (answered by jim_thompson5910)

I have to graph this equation: f(x)=x^2(x+2)(x-1) I know that x-intercepts are -2,+1 (answered by Solver92311,ikleyn)

Not sure if this is in the right section, but hoping for some help. I have this question (answered by Fombitz)