Question

select the correct answer.

what happens to the graph of (y = |x|) when the equation changes to (y = |x| + 6)?

• the graph shifts left 6 units.
• the graph shifts right 6 units.
• the graph shifts up 6 units.
• the graph shifts down 6 units.

Explanation:

🆕 New Concept Discovered: Transforming Functions
Moving a graph up, down, left, or right.

Step 1: Analyze the change in the equation

We start with the parent function:

$$ y = |x| $$

The equation is changed to:

$$ y = |x| + 6 $$

This change adds a constant value of \( 6 \) to the output of the original function.

Step 2: Determine the geometric effect

When we add a positive constant \( k \) to the outside of a function, \( y = f(x) + k \), every \( y \)-coordinate increases by \( k \) units.

• Adding \( 6 \) to the outside of the function shifts the entire graph vertically upward by \( 6 \) units.
• If it were inside the absolute value, like \( y = |x + 6| \), it would shift the graph horizontally.

Therefore, the graph of \( y = |x| + 6 \) is the graph of \( y = |x| \) shifted up \( 6 \) units.

Answer:

The graph shifts up 6 units.