Question

Use the image to answer the question. Which absolute value equation creates the lower function in the graph? Be sure to consider the scales of the x- and y-axis when evaluating the question. (1 point) Responses y=2|x|−2 y equals 2 Start Absolute Value x End Absolute Value minus 2 y=|x|−4 y equals Start Absolute Value x End Absolute Value minus 4 y=|x−4|−1 y equals Start Absolute Value x minus 4 End Absolute Value minus 1 y=12|x|−4

Answer 1

To determine which absolute value equation corresponds to the lower function in the graph, we need to analyze each option in terms of its vertical position (y-value) and the transformations involved:

1. **y = 2|x| - 2**: This function has a vertical stretch of 2 and shifted down by 2.
2. **y = |x| - 4**: This function is vertically shifted down by 4.
3. **y = |x - 4| - 1**: This function is shifted to the right by 4 and down by 1.
4. **y = 12|x| - 4**: This function has a vertical stretch of 12 and is shifted down by 4.

Assessing these equations:

- The first option would be more positive than the others due to the vertical stretch of 2 and starting at (0, -2).
- The second option starts at y = -4, which is lower than the first.
- The third option, y = |x - 4| - 1, starts from (4, -1), which is not lower than any of the previous functions.
- The fourth option starts at (0, -4), making it similar to the second option due to the vertical stretch.

From this analysis, the equation **y = |x| - 4** creates the lower function because it has the intercept at the lowest y-value of -4 for a wider span than the others, indicating it has the greatest downward shift without additional vertical stretch.

So the answer is: **y = |x| - 4**.