The graph given below represents which of the following function?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(y = |x - 1| + 1\)
The graph is V-shaped with its lowest point (the vertex) at (1, 1). The graph of \(y = |x - h| + k\) is a V with vertex at (h, k), so here \(h = 1\) and \(k = 1\):
\(y = |x - 1| + 1\)
The other marked points agree:
\(x = 0:\quad y = |0 - 1| + 1 = 2\)
\(x = 2:\quad y = |2 - 1| + 1 = 2\)
These are the points (0, 2) and (2, 2) marked on the graph.
Why the other options are incorrect
Option (1) \(y = |x + 1|\) — Incorrect. Its vertex is at (−1, 0); \(|x + 1|\) shifts the V to the left, not the right.
Option (2) \(y = |x + 1| + 1\) — Incorrect. Its vertex is at (−1, 1), and at \(x = 0\) it gives \(y = 2\) but at \(x = 1\) it gives 3, not 1.
Option (4) \(y = |x + 1| - 1\) — Incorrect. Its vertex is at (−1, −1), and at \(x = 0\) it gives 0, not 2.