precalculus

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analyzethe graph of the function

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-1)(x+1)^3

  • precalculus -

    y-intercepts (when x=0): (0,1)
    x-intercepts: (-1,0) and (1,0)

    end behavior: y decreases forever; approaches y = -x^4

    Turning points: f is of degree 4, so a max of 3 turning points
    In fact, it only has one at x = 1/2

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