Question

How is the graph of the parent function, y = √x transformed to produce the graph of y = -2√x?

a) It is translated horizontally by 2 units and reflected over the x-axis.
b) It is translated horizontally by 2 units and reflected over the y-axis.
c) It is horizontally compressed by a factor of 2 and reflected over the x-axis.
d) It is horizontally compressed by a factor of 2 and reflected over the y-axis.

Answer 1

The graph of the parent function y = √x can be transformed to produce the graph of y = -2√x by horizontally compressing it by a factor of 2 and reflecting it over the x-axis.

Step-by-step explanation:

The graph of the parent function y = √x can be transformed to produce the graph of y = -2√x. To do this, we need to apply two transformations. First, the graph is reflected over the x-axis, which means that every point on the original graph will have its y-coordinate negated. Second, the graph is vertically compressed by a factor of 2, meaning that the y-coordinates of all points on the graph will be multiplied by 2. Therefore, the correct answer is (c) It is horizontally compressed by a factor of 2 and reflected over the x-axis.