Answer:
- reflection over the x-axis
- translate right 2 units
- translate down 3 units
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).
Application
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
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The attached graph shows a function f(x) (red) and the transformed function (blue).