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The function f(x) = x^3 is transformed to f(x) = 4x^3. Which statement describes the graph of the transformed function?
A. The graph was translated up by 4 units.
B. The graph was stretched horizontally by a factor of 4.
C. The graph was translated down by 4 units.
D. The graph was stretched vertically by a factor of 4.

Respuesta :

Answer: Option D.

Step-by-step explanation:

The translation is defined as

[tex]g(x)=kf(x)[/tex]

Where, k is stretch factor.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

It is given that,

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

After transformation the function becomes

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

here, k=4>1, so the graph was stretched vertically by a factor of 4.

Therefore, the correct option is D.

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