38. Graph y=|2 x+1|
Answer
\(\boxed{\text{The graph of the function } y=|2x+1| \text{ is a V-shaped graph with the vertex at } x=-\frac{1}{2}. \text{ The slope of the lines forming the V is 2. The graph is symmetric with respect to the vertical line } x=-\frac{1}{2}.}\)
Step 1 ：The function given is \(y=|2x+1|\). This is an absolute value function, which will have a V shape.
Step 2 ：The vertex of the V will be at the point where the expression inside the absolute value equals zero. In this case, that would be at \(x=-\frac{1}{2}\).
Step 3 ：The slope of the lines forming the V will be 2, because that is the coefficient of x inside the absolute value.
Step 4 ：Plot the function using these values to get the graph.
Step 5 ：\(\boxed{\text{The graph of the function } y=|2x+1| \text{ is a V-shaped graph with the vertex at } x=-\frac{1}{2}. \text{ The slope of the lines forming the V is 2. The graph is symmetric with respect to the vertical line } x=-\frac{1}{2}.}\)
