contestada

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.)

Respuesta :

lublana

Answer with Step-by-step explanation:

We are given function

[tex]f(x)=x^2(x-2)(x-2)[/tex]

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

[tex]x^2(x-2)(x+2)=0[/tex]

[tex]x=0[/tex]

[tex]x-2=0[/tex]

x=2

[tex]x+2=0[/tex]

[tex]x=-2[/tex]

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

To find the y-intercept

Substitute x=0

[tex]y=0[/tex]

y-intercept:(0,0)

Otras preguntas