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he graph of y = | x | is translated down 5 units and right 4 units. What is the equation of the new graph?

Question

he graph of y = | x | is translated down 5 units and right 4 units. What is the equation of the new graph?

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Solution

The equation of the new graph is y = |x - 4| - 5.

Here's the step-by-step explanation:

  1. The original equation is y = |x|. This is the absolute value function, which creates a V-shaped graph.

  2. When we say the graph is translated down 5 units, it means we subtract 5 from y. So, y = |x| becomes y = |x| - 5.

  3. When we say the graph is translated right 4 units, it means we subtract 4 from x inside the absolute value. So, y = |x| - 5 becomes y = |x - 4| - 5.

So, the equation of the new graph after the translations is y = |x - 4| - 5.

This problem has been solved

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