Question

Analyze the polynomial function

​f(x)equals=x squared left parenthesis x minus 2 right parenthesis left parenthesis x plus 2 right parenthesis x2(x−2)(x+2)

using parts​ (a) through​ (e).

a) Determine the end behavior of the graph of the function.

The graph of f behaves like

yequals=nothing

for large values of

StartAbsoluteValue x EndAbsoluteValuex.

​(b) Find the​ x- and​ y-intercepts of the graph of the function.

The​ x-intercept(s) is/are

nothing.

​(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only​once.)

The​ y-intercept is

nothing.

​(Simplify your answer. Type an integer or a​ fraction.)

Answer 1

Answer with Step-by-step explanation:

We are given function

$f(x)=x^2(x-2)(x-2)$

a.From given we can see that

When x approaches to infinity then y also approaches infinity.

When x approaches-infinity then y  also approaches infinity.

b.To find the x-intercept

Substitute y=0

$x^2(x-2)(x+2)=0$

$x=0$

$x-2=0$

x=2

$x+2=0$

$x=-2$

x-intercept:(0,0),(2,0),(-2,0)

To find the y-intercept

Substitute x=0

$y=0$

y-intercept:(0,0)