SOLUTION: x- and y intercept and horizontal and vertical asymptotes of this rational function: y = (1/6)(x+2)^3(x-1)^2(6-x) I think the x intercepts must be (-2,0)(+1,0) and (+6,0)

Algebra ->  Functions -> SOLUTION: x- and y intercept and horizontal and vertical asymptotes of this rational function: y = (1/6)(x+2)^3(x-1)^2(6-x) I think the x intercepts must be (-2,0)(+1,0) and (+6,0)       Log On


   

Question 912267: x- and y intercept and horizontal and vertical asymptotes of this rational function:
y = (1/6)(x+2)^3(x-1)^2(6-x)
I think the x intercepts must be (-2,0)(+1,0) and (+6,0)
I understand there is no asymptotes but is there a y-intercept? and how would I go about graphing such a function?
Thank you
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Polynomial equation in factored form.
x-intercepts are readable directly from the factors: -2, 1, 6.
y-intercept is y where x=0. y=%281%2F6%29%282%5E3%29%28-1%29%5E2%286%29, y=8.

Do no confuse polynomial functions with rational functions! You say you understand that the equation has no asymptotes. A polynomial function is defined for all x values and is continuous everywhere. A rational function will have an expression of x in the denominator, and this causes some effect (in some cases) on sign of the function and also forces either a missing value for y or a vertical asymptote.

How to Graph:
The roots or x-intercepts make specific intervals on the x-axis. The graph will either touch or cross the x axis at the roots. Check the sign of y for each interval to know if that interval has positive y values or negative y values; and this helps you to sketch the graph.

Something is wrong with this graph....
graph%28300%2C300%2C-6%2C7%2C-10%2C10%2C%281%2F6%29%28x%2B2%29%5E3%28x-1%29%5E2%286-x%29%29
The graph seems to be displaying wrongly.