To determine the correct transformation from a solid-line graph to a dotted-line graph, we need to analyze the changes in the graph's appearance, particularly focusing on the horizontal stretch or compression.
- Horizontal Stretch: This indicates that the graph is made wider. If the factor \( k \) is greater than 1, it is a stretch.
- Horizontal Compression: This indicates that the graph is made narrower. If the factor \( k \) is between 0 and 1, it is a compression.
The factor \( k \) tells us how much the transformation affects the width. If \( k = 2 \), there’s a stretch, and if \( k = 0.5 \), there’s a compression.
Without a visual or additional context, the described options can only be analyzed generally. Here’s a guideline:
- If the graph appears to be wider (more spaced out), it's a "horizontal stretch" with \( k > 1 \).
- If the graph appears to be narrower (more compressed), it's a "horizontal compression" with \( k < 1 \).
Given the provided options, if you observe that the graph is narrower (compressed) and the factor is \( 0.5 \), then the correct choice would be:
Horizontal compression with a factor k = 0.5.
If the graph is wider and the factor shown is \( 2 \), then you would select one of the options indicating a stretch with \( k = 2 \). Please choose based on your visualization of the graph transformation.
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