Short Answer 
The function ( f(x) = -|x + 2| ) takes the absolute value of ( (x + 2) ) and makes it negative, resulting in a downward-opening graph. Key points include ( (-2, 0) ), ( (-4, -2) ), and ( (0, -2) ), which are used to sketch an inverted “V” shape on a coordinate system.
Step 1: Understand the Absolute Value Function
The given function is represented as f(x) = -|x + 2|. This means the function takes the absolute value of (x + 2), which will always yield a non-negative result, and then makes it negative. The graph of this function will open downward because of the negative sign in front of the absolute value.
Step 2: Determine Key Points
To plot the graph effectively, we identify crucial points from the function. The values of f(x) at specific x coordinates are essential:
- For x = -2, f(-2) = 0
- For x = -4, f(-4) = -2
- For x = 0, f(0) = -2
These points give us a foundation for drawing the graph.
Step 3: Sketch the Graph
Now, using the identified points (-2, 0), (-4, -2), and (0, -2), we can sketch the graph. Start by plotting these key points on a coordinate system and connect them smoothly, ensuring the graph opens downwards. The overall shape will be a V, inverted due to the negative sign in front of the absolute value function.