Final answer:
Multiplying the square root of x by 1/2 results in a vertical compression of the function, not a stretch, as the factor 1/2 is less than 1. This transformation scales down y-values, making the graph closer to the x-axis.
Step-by-step explanation:
The question is asking whether the expression 1/2 times the square root of x represents a vertical stretch. This concept pertains to the transformations that can be applied to the graph of a function. In the case of the given expression, vertical stretch refers to a transformation that multiplies all y-values of a function by a constant factor greater than 1, causing the graph to stretch away from the x-axis.
If we apply the multiplier 1/2 to the square root function, we are actually scaling the y-values by a factor of 1/2. This leads to a transformation known as a vertical compression, not a stretch, because the factor is less than 1. Therefore, each point on the graph of the square root function will be half as far from the x-axis as before the transformation. This is true regardless of the value of x, meaning that the response does not depend on the value of x.
The correct option would be B. No, because the multiplication by 1/2 results in a vertical compression.