The graph of f(x) = |x| is transformed to g(x) = |x + 1| – 7. On which interval is the function decreasing?

A) (–∞, –7)
B) (–∞, –1)
C) (–∞, 1)
D) (–∞, 7)

I put D but i'm not sure if it right

To determine the interval on which the function g(x) = |x + 1| - 7 is decreasing, we need to understand the behavior of the absolute value function and how it is transformed.

The absolute value function, f(x) = |x|, can be divided into two intervals based on the sign of x:
1. For x ≥ 0, f(x) = x.
2. For x < 0, f(x) = -x.

Now let's understand the transformation applied to f(x) to obtain g(x):
1. We have (x + 1) instead of x inside the absolute value function, which means that the graph of g(x) will be shifted one unit to the left compared to f(x).
2. We subtract 7 from the absolute value function, which means the entire graph of g(x) will be shifted 7 units downward.

Considering these transformations, we can now determine the interval on which g(x) is decreasing.

In the graph of f(x) = |x|, the function is decreasing on the interval (-∞, 0) since the values of x become more negative as we move from left to right.

Applying the transformations to g(x), the interval on which g(x) is decreasing is obtained by shifting the interval (-∞, 0) one unit to the left: (-∞, -1). Therefore, the correct answer is B) (–∞, –1).