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3. Consider a function f(x) = |x|. A second function g(x) is the result of translating f(x) by 5 units in the negative y-direction (downward), and 3 units in the positive x-direction (to the right). Write the equation of g(x)

Sagot :

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The translated function is:

g(x) = |x  + 3| - 5

How to get the translated function?

The parent function is f(x) = |x|, and we need to translate it.

Remember that:

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 of 3 units to the right and 5 units down is written as:

g(x) = f(x + 3) - 5 = |x  + 3| - 5

That is the translated function.

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

https://brainly.com/question/2972832

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