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for the function F(x)=(x-2)2(x+4) A: find all intercepts B: determine the end behavior C: determine the zeros of the function and their multiplicity

for the function F(x)=(x-2)2(x+4) A: find all intercepts B: determine the end behavior C: determine the zeros of the function and their multiplicity

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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for the function F(x)=(x-2)2(x+4)

A: find all intercepts

B: determine the end behavior

C: determine the zeros of the function and their multiplicity

Expert Solution
Step 1

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.

y=\left(x-2\right)^2\left(x+4\right)

to find the x-intercepts take y=0

\left(x-2\right)^2\left(x+4\right)=0

\left(x-2\right)^2=0,\:\:\:\:\:\:\:\:\:\:x+4=0

x-2=0,\:\:\:\:\:\:\:\:\:\:x=-4

x=2,\:\:\:\:\:\:\:\:\:\:x=-4

{\color{Red} \mathrm{X\:Intercepts}:\:\left(2,\:0\right),\:\left(-4,\:0\right)}

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