Question

1-Variable Equations & Inequalities Unit Test
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Question
Use the image to answer the question.

Graph of a solid V-shaped line and a dotted V-shaped line on a coordinate plane with axes from negative 7 to 7.

Which absolute value equation creates the lower function in the graph?

(1 point)
Responses

y=|x|−6
y equals Start Absolute Value x End Absolute Value minus 6

y=2|x|−6
y equals 2 Start Absolute Value x End Absolute Value minus 6

y=3|x|−3
y equals 3 Start Absolute Value x End Absolute Value minus 3

y=|x−3|−3

Answer 1

To determine which absolute value equation corresponds to the lower function in the graph, we need to analyze the information.

1. A solid line typically represents an equation that is inclusive (≥ or ≤) while a dotted (or dashed) line indicates a strict inequality (< or >).
2. The shape of the absolute value function is V-shaped. The general form of an absolute value function is \( y = a|x - h| + k \), where (h, k) is the vertex of the V.

Given the options:

1. \( y = |x| - 6 \) - This function has its vertex at (0, -6). The shape will be a V that opens upwards starting at -6 on the y-axis.
2. \( y = 2|x| - 6 \) - This function also has its vertex at (0, -6) but opens more steeply than the first option.
3. \( y = 3|x| - 3 \) - This function has its vertex at (0, -3) and also opens steeper than the first option but starts from a higher point than -6.
4. \( y = |x - 3| - 3 \) - This has its vertex at (3, -3) and will not correspond to a lower function as it shifts away from the origin.

Among these options, the function that creates the lower V-shaped function is:

**\( y = |x| - 6 \)**

If the graph shows a lower function that starts at -6 (as the question suggests), this is the correct option.