Graph each polynomial function. Factor first if the expression is not in factored form. f(x)=x^{2}(x+1)(x-1)

Maiclubk 2021-01-22 Answered
Graph each polynomial function. Factor first if the expression is not in factored form.
f(x)=x2(x+1)(x1)
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Expert Answer

aprovard
Answered 2021-01-23 Author has 94 answers

f(x)=x2(x+1)(x1) The function in factored form
The function has three zeros 0, -1, and 1
So, the graph of f(x) crosses the x-axis at (0,0), (-1,0), and (1,0)
To find the y-intercept, substitute 0 for x in f(x)
f(x)=x2(x+1)(x1)
f(0)=(0)2(0+1)(01) Substitute 0 for x
=0
So, the function f(x) crosses the y-axis at (0,0)
x2xx=x4
The leading coefficient is 1
Since the leading coefficient is positive and the function f(x) of degree 4 (even degree)
So, the end behavior is
x,f(x)
x,f(x)
See the graph below
image

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