Respuesta :

Ashraf82

The equation for f(x) = x³ after being translated to the left 6 units is

f(x + 6) = (x + 6)³

The equation for f(x) = x³ after being translated up 4 units is

f(x) + 4 = x³ + 4

The equation for f(x) = x³ after being translated to left 6 units and

up 4 units is f(x + 6) + 4 = (x + 6)³ + 4

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  

∵ f(x) = x³

∵ f(x) is translated left 6 units

- By using the second rule above add x by 6

∴ The equation will be f(x + 6)

∴ f(x + 6) = (x + 6)³

∵ f(x) = x³

∵ f(x) is translated up 4 units

- By using the third rule above add f(x) by 4

∴ The equation will be f(x) + 4

∴ f(x) + 4 = x³ + 4

The equation for f(x) = x³ after being translated to the left 6 units is

f(x + 6) = (x + 6)³

The equation for f(x) = x³ after being translated up 4 units is

f(x) + 4 = x³ + 4

The equation for f(x) = x³ after being translated to left 6 units and

up 4 units is f(x + 6) + 4 = (x + 6)³ + 4

Learn more:

You can learn more about transformation in brainly.com/question/2415963

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