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

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

1 answer

Without the images to analyze, I can provide general guidance on how to choose the correct response based on the characteristics of the graphs.

To determine whether the transformations involve vertical stretches or compressions, you should look at the shape of the curves in relation to their parent functions.

  • Vertical Stretches: If the curves appear "taller" or more elongated compared to the parent functions, they are experiencing vertical stretches. This typically happens when the transformation factor (k) is greater than 1.

  • Vertical Compressions: If the curves are "flatter" or squished down compared to the parent functions, they are undergoing vertical compressions. This occurs when the transformation factor (k) is between 0 and 1.

  • Same or Different Factors of k: You would need to analyze the steepness and height of the curves to determine if they share the same stretch/compression factor. If one curve is stretched more than the other, they would have different k values.

Based on your provided responses, if both graphs appear to stretch upward, then the correct choice would reflect that they are both "vertical stretches." Conversely, if they are flatter, the choice should denote "vertical compressions."

Based on this guidance, you will need to make your selection. If both graphs exhibit similar stretching or compression characteristics with the same factor, then select that option. Otherwise, choose the one indicating different factors if applicable.