Respuesta :

Ashraf82

The equation of the function is g(x) = Ix - 7I + 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) = IxI

∵ f(x) is shifted right 7 units

- By using the first rule above change x to x - 7

∵ f(x) is shifted up 4 units

- By using the third rule above change f(x) to f(x) + 4

∵ g(x) is the graph of f(x) but shifted right 7 units and shifted up 4 units

∴ g(x) = Ix - 7I + 4

The equation of the function is g(x) = Ix - 7I + 4

Learn more:

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

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facundo3141592

The equation of the translated function will be:

g(x) = |x - 7| + 4

How to shift a function?

There are two types of translations:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

  • If N is positive, the shift is to the left.
  • If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

  • If N is positive, the shift is upwards.
  • If N is negative, the shift is downwards.

Then, a translation right of 7 units and up 4 units is written as:

g(x) = f(x - 7) + 4

Replacing the actual function f(x) we get:

g(x) = |x - 7| + 4

If you want to learn more about translations, you can read:

https://brainly.com/question/24850937

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