Graph each polynomial function. Factor first if the expression is not in factored form. f(x)=2x^{3}(x^{2}−4)(x−1)

Brittney Lord 2020-11-20 Answered
Graph each polynomial function. Factor first if the expression is not in factored form.
f(x)=2x3(x24)(x1)
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Expert Answer

FieniChoonin
Answered 2020-11-21 Author has 102 answers

Step 1
f(x)=2x3(x24)(x1)
f(x)=2x3(x2)(x+2)(x1) The function in factored form
The function has four zeros 0,2,-2 and 1
So, the graph of f(x) crosses the x-axis at (0,0), (2,0), (-2,0) and (1,0)
To find the y-intercept, subtitute 0 for x in f(x)
f(x)=2x3(x24)(x1)
f(0)=2(0)3(024)(01) Substitute 0 for x
=0
So, the function f(x) crosses the y-axis at (0,0
Step 2 2x3x2x=2x6
The leading coefficient is 2
Since the leading coefficient is positive and the function f(x) of degree 6 (even degree)
So, the end behavior is
x,f(x)
x,f(x)

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