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Let the graph of g be a translation 6 units down followed by a reflection in the x -axis of the graph of f(x) = |x|. Write a rule for g

Respuesta :

MrRoyal

The rule of the function g is g(x) = -|x - 6|

How to write the rule for the function g?

The function is given as:

f(x) = |x|

The transformations are given as:

  • A translation 6 units down
  • A reflection in the x-axis of the graph

The above transformations are represented as:

A translation 6 units down:

f(x - 6)

This gives

f'(x) = |x - 6|

A reflection in the x-axis of the graph

f"(x) = -f(x)

This gives

f''(x) = -|x - 6|

So, we have:

g(x) = -|x - 6|

Hence, the rule of the function g is g(x) = -|x - 6|

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