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The graph of � = ∣ � ∣ y=∣x∣y, equals, vertical bar, x, vertical bar is shifted down by 9 99 units and to the right by 4 44 units. What is the equation of the new graph?

User Ritchy
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1 Answer

5 votes

Answer:

y = |x - 4| - 9.

Step-by-step explanation:

To shift the graph of y = |x| down by 9 units and to the right by 4 units, we can follow these steps: 1. Recall that shifting a graph involves adding or subtracting values to the original equation. To shift the graph down by 9 units, we will subtract 9 from the original equation. To shift the graph to the right by 4 units, we will subtract 4 from the variable x. 2. Apply the shifts to the equation y = |x|. Subtracting 9 from the equation gives y = |x| - 9. Subtracting 4 from the variable x gives y = |x - 4| - 9. 3. Simplify the equation. The absolute value of (x - 4) represents the distance of x from 4 on the number line. So, the equation y = |x - 4| - 9 means that the y-coordinate is equal to the distance of (x - 4) from 0 on the number line, minus 9. 4. Therefore, the equation of the new graph, after shifting the original graph y = |x| down by 9 units and to the right by 4 units, is y = |x - 4| - 9.

User Aleksei Anufriev
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