Question

Here is the graph that represents a function. Which equation represents the function?

Option 1: f(x) = |x| - 1
Option 2: g(x) = |x - 1|
Option 3: h(x) = |x + 1|
Option 4: j(x) = |x| + 1

Answer 1

Option 3: h(x) = |x + 1| represents the function.

Step-by-step explanation:

The equation that represents the given graph is Option 3: h(x) = |x + 1|.

To verify this, we can analyze the graph. The graph has a V-shape and is symmetric about the y-axis. The vertex of the V-shape is at (0, 1), which corresponds to the point (x, f(x)) = (0, 1). The function h(x) = |x + 1| represents this behavior. When x = 0, h(x) = |0 + 1| = 1, which matches the vertex of the graph.

Therefore, Option 3: h(x) = |x + 1| is the correct equation that represents the function.