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?
Solution
The equation of the new graph is y = |x - 4| - 5.
Here's the step-by-step explanation:
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The original equation is y = |x|. This is the absolute value function, which creates a V-shaped graph.
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When we say the graph is translated down 5 units, it means we subtract 5 from y. So, y = |x| becomes y = |x| - 5.
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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.
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