Question

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

Answer 1

Horizontal translation → Reflection about x-axis → Vertical Translation

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.