Question 465712: For the function below, provide the following: (A)x-intercept(s) (B)y-intercept(s) (C)end behavior of the graph (D)graph of this function. Please show all of your work and submit your graph. f(x) = (x – 4)(x – 2)(x – 1)
I need some help please.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! For the function below, provide the following: (A)x-intercept(s) (B)y-intercept(s) (C)end behavior of the graph (D)graph of this function. Please show all of your work and submit your graph. f(x) = (x – 4)(x – 2)(x – 1)
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f(x) = (x – 4)(x – 2)(x – 1)
(A) To find x-intercepts (zeros), set f(x) =0, then solve for x
x-4=0
x=4
..
x-2=0
x=2
..
x-1=0
x=1
..
(B) To find y-intercept, set x=0, then solve for y
y=(-4)(-2)(-1)=-8
..
(C) End behavior:
You can see that for x>0, f(x)>0
The sign of f(x) switches every time we go thru zeros, 4, 2, & 1. (This happens when the factors are of odd multiplicity ;ie, 1, 3, 5 etc.)
(4, ∞), f(x)>0
(2, 4), f(x)<0
(1, 2), f(x)>0
(-∞, 1), f(x)<0
..
(D) Graphing:
See the following graph as a visual check on the answers
..
y)=x^3-7x^2+14x-8
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