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.

Question

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

Answer 1

To determine the type of transformation represented by the curves passing through the plotted points in the two graphs, we need to consider the nature of the transformations applied to the parent functions.

Vertical stretches and compressions are determined by a factor \( k \) in the transformation equation \( y = kf(x) \), where \( f(x) \) is the parent function. If \( |k| > 1 \), it indicates a vertical stretch, making the graph taller. If \( |k| < 1 \), it indicates a vertical compression, making the graph shorter.

Based on the description, the two graphs could depict different transformations depending on the variation in their stretched or compressed state. Without specific details on the function transformations, we cannot definitively state whether \( k \) is the same or different for both graphs. Therefore, the most appropriate general option is:

Both graphs represent vertical stretches or compressions, although they use different factors of \( k \).

So the correct response would be: Both graphs represent vertical stretches or compressions, although they use different factors of k.