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

Horizontal translation → Reflection about x-axis → Vertical Translation

Step-by-step explanation:

We are given the function f(x) = |x|.

This function is transformed to the new function given by g(x) = - |x+4| - 1.

So, we see that,

1. Translation of 4 units to the left is applied, which changes f(x) = |x| to |x+4|.

2. Reflection about x-axis is applied, which changes |x+4| to - |x+4|.

3. Finally, translation of 1 unit downward is applied, which changes - |x+4| to g(x) = - |x+4| -1.

Hence, the sequence of transformation applied to obtain g(x) from f(x) is Horizontal translation → Reflection about x-axis → Vertical Translation.

the cat is blue because the probability of extension towards the prefix of the diameter of the circle could only mathematically equal to the sum of the roots of the carrots from   your garden.

step-by-step explanation:

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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