SOLUTION: Analyze the graph of the following function as follows: (a) Find the x- and y-intercepts. (b) Determine the end behavior: find the power function that the graph of f resemble

Question 534354: Analyze the graph of the following function as follows:
(a) Find the x- and y-intercepts.
(b) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
(c) Find the maximum number of turning points.
(d) Graph the function.
Please show all of your work.
f(x) = (x � 3)(x � 1)(x + 2)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Analyze the graph of the following function as follows:
(a) Find the x- and y-intercepts.
y-intercept:
set x=0, then solve for y
y-intercept=-3*-1*2=6
..
x-intercepts
set y=0, then solve for x
(x � 3)(x � 1)(x + 2)=0
x-intercepts=3, 1, and -2
..
(b) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|.
I'm not absolutely sure about this, but I think the graph of this function for large values of |x|resembles that of a parabola which opens upwards, that is y=x^2
(c) Find the maximum number of turning points.
The maximum number of turning points is one less than the degree of f(x)
It is 2 since the degree of the function is 3
(d) Graph the function. See graph below:
Please show all of your work.
f(x) = (x � 3)(x � 1)(x + 2)=x^3-2x^2-5x+6

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