What is the shape of the graph y = sqrt(x)?

The graph of \( y = \sqrt{x} \) is a curve that starts at the origin and rises to the right.

In more detail, the graph of \( y = \sqrt{x} \) represents the set of all points \((x, y)\) where \( y \) is the positive square root of \( x \). This means that for every non-negative value of \( x \), there is a corresponding \( y \) value that is the square root of \( x \). The graph starts at the origin (0,0) because the square root of 0 is 0. As \( x \) increases, \( y \) also increases, but at a decreasing rate. This creates a curve that rises to the right, becoming less steep as \( x \) gets larger.

The graph is only defined for \( x \geq 0 \) because the square root of a negative number is not a real number. Therefore, you will not see any part of the graph in the left half of the coordinate plane. The shape of the graph is a gentle curve that gets flatter as you move to the right. This is because the rate of increase of the square root function slows down as \( x \) increases. For example, the square root of 1 is 1, the square root of 4 is 2, and the square root of 9 is 3, showing that larger \( x \) values result in smaller incremental increases in \( y \).

Understanding the shape of this graph is important for solving problems involving square roots and for visualising how the function behaves. It helps to know that the graph will always be in the first quadrant and will never dip below the x-axis or extend into the negative x-values.