What shape does the graph of y represent when y is equal to the square root of A - x²?

The equation ( y = \sqrt{A - x^2} ) describes the top half of a circle. To understand this, we can rearrange the equation to make the relation to a circle more evident. If we square both sides, we get ( y^2 = A - x^2 ), which can be rewritten as ( x^2 + y^2 = A ). This is the equation of a circle centered at the origin with a radius of ( \sqrt{A} ).

The original equation ( y = \sqrt{A - x^2} ) only considers the positive values of ( y ), which corresponds to the upper half of the circle. Therefore, the graph does not exhibit the full circular shape since it does not include negative values of ( y ).

This reasoning clearly aligns with the choice indicating that the graph represents a semicircle on the top half.