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grandymaker [24]
2 years ago
9

What transformation of the parent function f(x) is made to get −f(x−2)−3?

Mathematics
1 answer:
Vladimir [108]2 years ago
6 0

Answer:

  • reflection over the x-axis
  • translate right 2 units
  • translate down 3 units

Step-by-step explanation:

Horizontal translation of the graph of a function is accomplished by replacing x with (x-h) for translation h units to the right. Vertical translation of the graph is accomplished by adding the amount of translation to the function value: f(x)+k translates the graph k units upward.

Reflection of a function over the x-axis is accomplished by changing the sign of every function value: -f(x).

<h3>Application</h3>

We observe that f(x) has been transformed by ...

  • multiplying by -1 to get -f(x)
  • replacing x with (x -2) to get -f(x -2)
  • adding -3 to the function value to get -f(x -2) -3

The effect of these transformations is (correspondingly) ...

  • reflection over the x-axis
  • translate right 2 units
  • translate down 3 units

__

The attached graph shows a function f(x) (red) and the transformed function (blue).

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