Which equation for the absolute value equation creates the upper function in the graph?

Question

(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 plus 3 End Absolute Value

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

y=|x|−3

Answer 1

To determine which equation creates the upper function in the graph, we need to analyze the effect of each equation on the absolute value function \( y = |x| \):

1. \( y = |x| + 3 \): This graph represents the absolute value function shifted upward by 3 units. So, it is definitely above the basic absolute value function \( y = |x| \).

2. \( y = |x + 3| \): This translates the basic absolute value function to the left by 3 units. The shape remains the same and it does not move it up or down.

3. \( y = |x - 3| \): This translates the basic absolute value function to the right by 3 units. Similar to the second option, the shape remains unchanged.

4. \( y = |x| - 3 \): This graph represents the absolute value function shifted downward by 3 units, making it lower than \( y = |x| \).

The equation that creates the upper function among the given options is:

\( y = |x| + 3 \).