The graph of y = |x – 1| is translated 3 units left and 2 units down. What is the equation of the new graph?
Question
The graph of y = |x – 1| is translated 3 units left and 2 units down. What is the equation of the new graph?
Solution
The equation of the new graph is y = |x + 2| - 2.
Here's the step by step explanation:
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The original equation is y = |x – 1|.
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When a graph is translated 3 units to the left, we add 3 to the x values in the equation. So, |x – 1| becomes |x – 1 + 3|, which simplifies to |x + 2|.
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When a graph is translated 2 units down, we subtract 2 from the y values in the equation. So, y = |x + 2| becomes y = |x + 2| - 2.
So, the equation of the new graph is y = |x + 2| - 2.
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