Ask a New Question
Menu

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 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, 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.

1 answer

To determine the transformation represented by the graphs, we need to analyze the nature of the plotted points and their locations related to their parent functions.

  • Vertical Compression occurs when the points of a graph are closer to the x-axis compared to the parent function. This is indicated by a factor \( k < 1 \).
  • Vertical Stretch occurs when the points of a graph are further away from the x-axis compared to the parent function. This is indicated by a factor \( k > 1 \).

Given that both sets of graphs represent transformations from their respective parent functions, we can infer from the behavior of the points:

  1. If both graphs are displaced vertically compared to their parent functions but follow a similar pattern (example: straight-line, parabolic), but stay within a certain range without extending too far upwards or downwards, this demonstrates a vertical compression.

  2. If points are further away from the horizontal center (the x-axis) compared to their parent function's placement, then it suggests a vertical stretch.

Since the question states that both graphs represent vertical compressions and since they can have different factors of \( k \), we can conclude that the most fitting response is:

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