Question

Use the image to answer the question. Which equation for the absolute value equation creates the upper function in the graph? (1 point) Responses y=|x|+3 y equals Start Absolute Value x End Absolute Value plus 3 y=|x−3| y equals Start Absolute Value x minus 3 End Absolute Value y=|x|−3 y equals Start Absolute Value x End Absolute Value minus 3 y=|x+3|

Answer 1

To determine which equation creates the upper function in a graph of absolute value equations, we can analyze each option based on how vertical shifts affect the graph.

1. y = |x| + 3: This represents the absolute value function shifted upward by 3 units. This will be an upper function compared to just y = |x|.

2. y = |x - 3|: This represents the absolute value function shifted to the right by 3 units. It does not affect the vertical position.

3. y = |x| - 3: This represents the absolute value function shifted downward by 3 units. This will be lower than y = |x|.

4. y = |x + 3|: This represents the absolute value function shifted to the left by 3 units. Again, this does not affect the vertical position like the first option.

Considering these transformations, the upper function in the graph is likely to be represented by y = |x| + 3 as it is the only equation that shifts the basic absolute value function up. Therefore, it is the correct response.