Questions: Below is the graph of y=x. Translate it to make it the graph of y=x-4+2.

Transcript text: Below is the graph of $y=|x|$. Translate it to make it the graph of $y=|x-4|+2$.

Solution

Solution Steps

Step 1: Horizontal Shift

The equation y = |x-4| represents a horizontal shift of the original graph y = |x|. Since it's x-4, the graph shifts 4 units to the _right_.

Step 2: Vertical Shift

The equation y = |x-4| + 2 introduces a vertical shift. The +2 indicates a shift 2 units _upward_.

Final Answer

The graph of y = |x-4| + 2 is obtained by taking the graph of y = |x|, shifting it 4 units to the right, and then 2 units up. The vertex will be at (4,2).

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