Determine the domain, range, zeros, y intercepts, end behavior, and intervals of increasing or decreasing of f(x) = x(x+4)(x+5)^3

Question

campbell_st · Answer

well do you have any thoughts... about the question... 

or have some answers...?

anonymous · Answer

i have the domain, range, and end behavior, but i don't know how to get the other parts

campbell_st · Answer

ok... so the zeros... 

the polynomial is factored

so you need to solve

x = 0

x+4 = 0

x +5 = 0

thats a start

anonymous · Answer

0, -4, -5, thanks! i have no idea what to do for y intercepts and I'm trying increasing/decreasing on my calculator but I'm still kinda confused on it

campbell_st · Answer

ok... so the y intercept is 0... 

since the product of the constants will give the y intercept

so the polynomial can be written as 

$$y = (x + 0)(x +4)(x + 5)^3$$

the constants are 0, 4 and 5^3

so their product is 

$$0 \times 4 \times 5^3= ?$$

what do you think

anonymous · Answer

that would equal 0

campbell_st · Answer

yep... so thats the y-intercept..

anonymous · Answer

thank you!! you're really smart and i appreciate how you are making me think and not just giving me the answer, it's really helpful

campbell_st · Answer

ok... so the function is an odd power... starting lower left and finishing upper right... 


so it looks something like this.... 


|dw:1389932526442:dw|

you'll probably need to use calculus to find the 1st derivatives.... and max and min values... 

and 2nd derivatives to find the points of inflexion