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.

Question

(1 point)
Responses

y=12|x|−4
y equals Start Fraction 1 over 2 End Fraction 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=2|x|−2
y equals 2 Start Absolute Value x End Absolute Value minus 2

y=|x|−4

Answer 1

To determine which absolute value equation represents the lower function in the graph, we need to analyze the equations given.

1. y = 12|x| - 4: This function has a steep slope due to the multiplier of 12 and starts at -4 on the y-axis.
2. y = (1/2)|x| - 4: This function has a gentle slope and starts at -4 on the y-axis. Since the slope is less steep, this function will be lower at many points compared to others with steeper slopes.
3. y = |x - 4| - 1: This has a V-shape starting at (4, -1). It's relatively low, but it rises as |x| increases outward.
4. y = |x| - 4: This function starts at -4 (at x=0) and has a less steep slope than some other functions.

Based on the shapes and intercepts of these functions, we can analyze the y-intercepts and general positions on the graph.

• The function that remains consistently below the others at the same scale is likely the one with the least steep slope and lowest starting point.

Comparing relative positions around (0,-4):

• The function y = (1/2)|x| - 4 has a consistently lower y-value compared to functions with steeper slopes, particularly around the axis.

Thus, the equation that creates the lower function in general terms is:

y = (1/2)|x| - 4