Use the images to answer the question.

Question

A curve passes through 7 plotted points on a coordinate plane with x and y axes ranging from negative 10 to 10 in unit increments. A curve passes through 4 plotted points on a coordinate plane with x-axis ranging from negative 9 to 9 in increments of 1 and y-axis ranging from negative 11 to 11 in increments of 1.
Both graphs represent transformations from their respective parent functions. Describe the transformation.

(1 point)
Responses

Both graphs represent vertical compressions, although they use different factors of k.
Both graphs represent vertical compressions, although they use different factors of k .

Both graphs represent vertical compressions, with the same factors of k.
Both graphs represent vertical compressions, with the same factors of k .

Both graphs represent vertical stretches, although they use different factors of k.
Both graphs represent vertical stretches, although they use different factors of k .

Both graphs represent vertical stretches, with the same factors of k.

Answer 1

To answer your question accurately, I would need to see the images of the graphs mentioned. However, based on the general concepts of transformations, here are some explanations for the options provided:

1. Vertical Compression: This occurs when a graph is transformed such that the y-values are multiplied by a factor \( k \) where \( 0 < k < 1 \), making the graph "squash" toward the x-axis.

2. Vertical Stretch: This happens when a graph is transformed so the y-values are multiplied by a factor \( k \) where \( k > 1 \), causing the graph to "stretch" away from the x-axis.

3. Factors of \( k \): The specific numerical value of \( k \) indicates how much compression or stretch is applied. Different factors of \( k \) mean that the two graphs are transformed by different amounts, even if they both undergo vertical compressions or stretches.

Based on these definitions:

• If both graphs are vertically compressed but with different \( k \) values, you would select the option indicating vertical compressions with different factors.
• If both graphs are vertically stretched with different \( k \) values, you would choose the appropriate option for stretches.

Without the images, I can't definitively say which option applies. You'll need to determine whether the curves appear to be stretched or compressed and whether the factors are the same or different based on the visual evidence. Choose the response that best matches the observed transformations of the curves in the images.