To transform the graph of y = √₃√(x - 4) into the graph of y = √₃√(2x - 4), we need to consider the two given transformations: stretching the graph horizontally by a factor of 2 and moving it right 4 units. First, let's consider the stretching. When we stretch the graph horizontally by a factor of 2, this means that for every x-value on the original graph, we will have half that x-value on the new graph. In other words, if we take a point (x, y) on the original graph, the corresponding point on the new graph will be (x/2, y). Next, let's consider the movement to the right by 4 units. This means that for every x-value on the original graph, we will have that x-value plus 4 on the new graph. So if we have a point (x, y) on the original graph, the corresponding point on the new graph will be (x + 4, y). Now, let's combine these two transformations. If we have a point (x, y) on the original graph, the corresponding point on the new graph after stretching by a factor of 2 and moving right 4 units will be ((x/2) + 4, y). Therefore, the graph of y = √₃√(x - 4) transformed into the graph of y = √₃√(2x - 4) is obtained by stretching the graph horizontally by a factor of 2 and moving it right 4 units. In other words, the correct answer is: The graph is stretched horizontally by a factor of 2 and then moved right 4 units.
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To transform the graph of y = √₃√(x - 4) into the graph of y = √₃√(2x - 4), we need to consider the two given transformations: stretching the graph horizontally by a factor of 2 and moving it right 4 units. First, let's consider the stretching. When we stretch the graph horizontally by a factor of 2, this means that for every x-value on the original graph, we will have half that x-value on the new graph. In other words, if we take a point (x, y) on the original graph, the corresponding point on the new graph will be (x/2, y). Next, let's consider the movement to the right by 4 units. This means that for every x-value on the original graph, we will have that x-value plus 4 on the new graph. So if we have a point (x, y) on the original graph, the corresponding point on the new graph will be (x + 4, y). Now, let's combine these two transformations. If we have a point (x, y) on the original graph, the corresponding point on the new graph after stretching by a factor of 2 and moving right 4 units will be ((x/2) + 4, y). Therefore, the graph of y = √₃√(x - 4) transformed into the graph of y = √₃√(2x - 4) is obtained by stretching the graph horizontally by a factor of 2 and moving it right 4 units. In other words, the correct answer is: The graph is stretched horizontally by a factor of 2 and then moved right 4 units.
