Ask a New Question
Menu

Use the attached image to answer the question. Interpret the key features of the graph. What type of transformation occurred from the parent function?

A. This is a vertical stretch of the parent function: y = x^2, due to the changes in the y-coordinates of each point.
B. This is a vertical stretch of the parent function: y = x^2, due to the changes in the x-intercept.
C. This is a vertical stretch of the parent function: y = x^2, due to the changes in the x-coordinates of each point.
D. This is a vertical stretch of the parent function: y = x^2, due to the changes in the y-intercept.

1 answer

To answer the question accurately, I would need to review the attached image of the graph you're referring to. However, since I cannot view images, I can guide you on how to interpret the key features of the graph and identify the type of transformation that likely occurred based on common transformations of the parent function, \( y = x^2 \).

When you analyze a graph relative to the parent function \( y = x^2 \):

  1. Vertical Stretch: If the graph of the function appears "stretched" vertically when compared to the parent function, this typically means that the coefficient in front of \( x^2 \) is greater than 1 (e.g., \( y = ax^2 \) with \( a > 1 \)).

  2. Changes in Points:

    • Y-coordinates: If the y-coordinates of the points have increased (or decreased) disproportionately according to a scaling factor, this indicates a vertical transformation.
    • X-coordinates: The x-coordinates do not change the vertical stretch or compression; rather, they determine the horizontal position of the graph.

  3. Intercepts: The y-intercept of the graph is the point where the function crosses the y-axis when \( x = 0 \). A vertical stretch will change how high or low this intercept is, but the x-intercept, where \( y = 0 \), mainly reflects how the function intersects the x-axis, not the type of vertical transformation.

Now, interpreting your options:

  • Options A and D both suggest that you are looking at the y-coordinates as the metric of transformation (which is accurate for discussing stretches).
  • Option B refers to changes in x-intercepts, which do not apply to vertical stretches.
  • Option C suggests changes in x-coordinates. This is irrelevant for identifying vertical transformations.

Based on this analysis, if the graph shows a vertical stretch regarding how it has changed from the parent function and you are focusing on y-changes, then A would be the most appropriate choice, as it refers directly to the y-coordinates increasing according to a vertical stretch.

If you have specific information on how the graph is transformed or any additional details, feel free to share that for more precise guidance.