The graph of the absolute function is the graph (b)
How to determine the graph of the absolute function
From the question, we have the following parameters that can be used in our computation:
f(x) = -0.5|x + 3| - 2
The above function is an absolute function transformed from the parent function f(x) = |x| as follows
1. Reflection across the x-axis;
This means that the graph will open down and it is indicated by the negative sign
i.e. f(x) = -|x|
2. Vertical stretch by a factor of 0.5
This means that the graph will be wider than the parant function and it is indicated by 0.5
i.e. f(x) = -0.5|x|
3. Horizontal shift to the left by 3 units
This means that the graph will move to the left of the origin by 3 units and it is indicated by + 3
i.e. f(x) = -0.5|x + 3|
4. Vertical shift down by 2 units
This means that the graph will move down the origin by 2 units and it is indicated by + 3
i.e. f(x) = -0.5|x + 3| - 2
Using the above as a guide, we have the following:
The graph is (b)
Question
Which of the following is the graph of f(x) = -0.5|x + 3| - 2