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 minus 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 plus 3

y=|x+3|

Answer 1

To determine which equation creates the upper function in the graph, we need to understand how the absolute value function affects the position of the graph vertically.

1. **y = |x| - 3**: This graph is shifted down 3 units.
2. **y = |x - 3|**: This graph is shifted to the right by 3 units, remaining at the same vertical level as the basic |x| function.
3. **y = |x| + 3**: This graph is shifted up 3 units, moving further away from the x-axis.
4. **y = |x + 3|**: This graph is shifted to the left by 3 units, but keeps the same vertical position as the basic |x| function.

Since you are looking for the equation that creates the upper function in the graph, the correct response would be:

**y = |x| + 3**.

This function shifts the absolute value graph upwards, making it the upper function compared to the others listed.