To determine the transformation from the solid-line graph to the dotted-line graph of the parabolas, we first need to identify the relationship between the x-values of points on both graphs.
If the dotted-line graph represents a horizontal compression of the solid-line graph, it means that the distance between the same y-value points on both graphs is reduced. When we say "horizontal compression with a factor k," it implies that the x-values of the dotted line are multiplied by a value greater than 1 to achieve the new positions.
Alternatively, if the dotted-line graph represents a horizontal stretch, the distance increases, meaning the x-values of the points on the dotted line are less than those on the solid line, thus moving them farther apart.
To assess the given options:
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Horizontal compression with a factor k = 0.5: This means the x-values of the dotted line are half of those on the solid line.
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Horizontal stretch with a factor k = 2: Here, the x-values of the dotted line are twice those of the solid line.
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Horizontal compression with a factor k = 2: This means the x-values of the dotted line are divided by a factor of 2, which is incorrect as it results in stretching, not compressing.
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Horizontal stretch with a factor k = 0.5: Again, this indicates compression rather than stretching since the points would come closer together.
To find the correct answer, you would analyze the plotted points on both graphs. Assuming you notice that the x-values of the new points on the dotted graph relate to those of the solid graph in a way that suggests the x-values of the dotted graph are halved, then the answer would be:
Horizontal compression with a factor k = 0.5.
If the x-values in the dotted graph are actually doubled compared to the solid line's x-values, then it would be:
Horizontal stretch with a factor k = 2.
Without seeing the graphs directly, the determination would need careful consideration of the x-values' adjustments. Based on typical transformations, if it looks like the graph is compressed horizontally,:
- The correct answer would be horizontal compression with a factor k = 0.5.
If the dotted-line graph expands the points away from the vertex, then the appropriate answer would likely involve a stretch factor.
Without the image, please use this guideline to select your answer based on your observations of the graph transformations.