The equation y = 0.5√x experiences vertical compression with a coefficient of 0.5, leading to a steeper and compressed graph compared to the standard square root function.
The provided equation is y = 0.5√x. To determine vertical stretch or compression, we compare it to the standard square root function y = √x. The presence of the coefficient 0.5 indicates a vertical compression.
Generally, when a constant 'a' is multiplied to a function, it leads to vertical stretch or compression. If 0 < a < 1, it compresses the graph vertically. Here, a = 0.5, indicating vertical compression.
The standard square root function √x has a smooth, upward-curving graph from the origin. When multiplied by 0.5, the entire graph is vertically compressed, making it steeper. Each y-value is halved, causing the function to rise more gradually.
In summary, the equation y = 0.5√x undergoes vertical compression due to the coefficient 0.5, resulting in a steeper and compressed graph compared to the standard square root function.