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Use the images to answer the 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 stretches, although they use different factors of k.
Both graphs represent vertical stretches, although they use different factors of k .

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

To determine the transformation represented by the curves on the coordinate planes as described, we need to analyze the nature of the transformations based on the provided information.

  1. Vertical Stretch vs. Compression:

    • A vertical stretch occurs when a function is multiplied by a factor greater than 1 (k > 1), making the graph taller.
    • A vertical compression occurs when a function is multiplied by a factor between 0 and 1 (0 < k < 1), making the graph shorter.

  2. Different Factors of k:

    • If both graphs represent the same type of transformation (either stretch or compression) but differ in the exact extent of that transformation (different values of k), then we would refer to them as having different factors of k.

  3. Same Factors of k:

    • If both graphs represent the same type of transformation and are transformed using the same factor of k, we would denote them as having the same factors of k.

Given the options provided, selecting one requires either visual confirmation or additional context that indicates the stretching or compressing nature and the specific factors involved.

Ultimately, without specific knowledge of the shape and nature of the graphs presented, the most appropriate answer format based on the descriptions would be:

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

This response would indicate an understanding that both transformations are of similar types, with variances in their intensity. If you have insight into the graphs' specifics, that would guide the exact response choice further.