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Write the resulting function f(x) = |x| translated left 2 units and translated up 3 units.

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Final answer:

The original function f(x) = |x| is first translated left 2 units by replacing x with (x+2), resulting in f(x) = |x+2|. After this, it is translated up by 3 units resulting in the final function: f(x) = |x+2| + 3.

Step-by-step explanation:

The original function given is f(x) = |x|. When we want to translate this function to the left by 2 units, we should replace 'x' with '(x+2)' resulting in a new function: f(x) = |x+2|. This shifts the function to the left on the x-axis by 2 units.

Similarly, To translate the function up by 3 units, we simply add 3 to the entire function, which gives us: f(x) = |x+2| + 3. This moves the function up on the y-axis by 3 units. So, the final resulting function after translating left 2 units and up 3 units is f(x) = |x + 2| + 3

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