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Consider the function f(x) = |x|. Write a function rule for g(x) which is a translation of f(x) left 3 units.

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Final answer:

The function g(x) which is a translation of f(x) = |x| left by 3 units is g(x) = |x + 3|. The graph of g(x) shifts every x-value from the original f(x) left by 3 units without changing the 'V' shape of the graph.

Step-by-step explanation:

To translate the function f(x) = |x| left by 3 units, we will apply the transformation rule which states that f(x - d) is the function translated right by d units, and f(x + d) is the function translated left by d units. In our case, we want to move the function f(x) left, so we will use f(x + d). Since we are moving 3 units to the left, d will be 3, making our new function g(x) = |x + 3|.

This translation affects the function in such a way that every x-value on the graph of f(x) is shifted 3 units to the left to create the graph of g(x). Where the original function f(x) was zero at x = 0, the translated function g(x) will now be zero at x = -3. Importantly, the shape of the graph remains the same; it still has its characteristic 'V' shape when graphed.

The function g(x) which is a translation of f(x) = |x| left by 3 units is g(x) = |x + 3|. The graph of g(x) shifts every x-value from the original f(x) left by 3 units without changing the 'V' shape of the graph.

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