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The graph of F(x), shown below, has the same shape as the graph of
G(X) = x^3, but it is shifted down 3 units. What is its equation?

Respuesta :

Ashraf82

The equation of F(x) is F(x) = x³ - 3

Step-by-step explanation:

Let us revise the translation

  • If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)  
  • If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)  
  • If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k  
  • If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k  

∵ The graph of F(x) has the same shape as the graph of

   G(x) but it is shifted down 3 units

- That means F(x) is the image of G(x) after translation 3 units down

∴ The graph of the function G(x) translated vertically down by 3 units,

   to give the graph of F(x) = G(x) - 3  

∵ G(x) = x³

∴ F(x) = x³ - 3

The equation of F(x) is F(x) = x³ - 3

Learn more:

You can learn more about the translation in brainly.com/question/2451812

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