Describe the transformation that takes f(x) =|x| to g(x)= -|x+4| -1

Translation 4 units to left, reflection about x-axis and then translation 1 unit up.

Step-by-step explanation:

We are given the applying some transformations to f(x) = |x| gives g(x) = -|x+4|+1.

Now, at the start f(x) is translated 4 units to the left i.e. f(x) is shifted 4 units to the left.

This gives us the new function as |x+4|.

Now, this new function is reflected about x-axis i.e. it is flipped across x-axis.

So, we get the new function - |x+4|.

Finally, we can see that - |x+4| is translated 1 units upwards i.e. it is shifted 1 unit up.

This gives us the required function g(x) = - |x+4| + 1 as shown below.

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step-by-step explanation: