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How do you translate the graph of f(x) = x3 left 4 units and down 2 units? Identify the equation of the graph
A. y= (x-4)^3 -2.
B. y=(x+4)^3 -2.
D. y=(x-2)^3 -4.

Respuesta :

Answer:

The correct option is B.

Step-by-step explanation:

The given function is

[tex]f(x)=x^3[/tex]

The translation of a function is defined as

[tex]g(x)=f(x+a)+b[/tex]

If a>0, then the graph of f(x) shift a units left and if a<0, then the graph of f(x) shift a units right.

If b>0, then the graph of f(x) shift b units up and if b<0, then the graph of f(x) shift b units down.

It is given that the graph of f(x) shifts 4 units left and 2 units down.  So, a=4 and b=-2.

[tex]g(x)=f(x+4)+(-2)[/tex]

[tex]g(x)=(x+4)^3-2[/tex]              [tex][\because f(x)=x^3][/tex]

[tex]y=(x+4)^3-2[/tex]

Therefore option B is correct.

MrRoyal

Transformation involves changing the form of a function.

The equation that translates f(x) 4 units left and 2 units down is [tex]y = (x + 4)^3 - 2[/tex]

The function is given as:

[tex]f(x) = x^3[/tex]

Translate left by 4 units.

So, we have:

[tex]f(x + 4) = (x + 4)^3[/tex]

Translate down by 2 units.

So, we have:

[tex]f(x + 4) - 2 = (x + 4)^3 - 2[/tex]

Rewrite as:

[tex]y = (x + 4)^3 - 2[/tex]

Hence, the equation that translates f(x) 4 units left and 2 units down is [tex]y = (x + 4)^3 - 2[/tex]

Read more about function transformation at:

https://brainly.com/question/1548871

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