• x-intercept(s)
  • y-intercept(s)
  • end behavior of the graph
  • graph of this function.
  • f(x)=4x^2(x-2)^3

    please help

    Expert Answers

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    Find the intercepts and discuss the end behavior for `f(x)=4x^2(x-2)^3`

    (1) The y-intercept occurs when x=0: So the y-intercept is 0.

    (2) The x-intercepts occur when y=0: By the zero product property f(x)=0 when either `4x^2=0` or `(x-2)^3=0` , so the two x-intercepts are 0 and 2.

    (3) f(x) is a polynomial of degree 5 with a positive leading coefficient. So `lim_(x->-oo)f(x)=-oo` and `lim_(x->oo)=oo`

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