Question

value: 3

match the items.
a. \\(y = \sqrt{x}\\)
b. \\(y = \sqrt{x} - 4\\)
c. \\(y = \sqrt{x} + 5\\)

1. orange graph
2. blue graph
3. red graph

Explanation:

Identify the vertex of the red graph

The red curve shown in the graph starts at the point \((0, -4)\).

Match the vertex to the function transformations

The parent function \(y = \sqrt{x}\) has its vertex at \((0, 0)\).
A vertical shift down by \(4\) units is represented by \(y = \sqrt{x} - 4\), which has its vertex at \((0, -4)\).
Therefore, the red graph corresponds to equation b.

Deduce the remaining matches

By standard vertical transformations:

• \(y = \sqrt{x}\) has its vertex at \((0, 0)\), which corresponds to the blue graph (not fully visible but standard parent position).
• \(y = \sqrt{x} + 5\) has its vertex shifted up by \(5\) units to \((0, 5)\), which corresponds to the orange graph.

Answer:

1. Orange graph: c
2. Blue graph: a
3. Red graph: b