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The graph of y=|x| is shifted down by 9 units and to the right by 4 units. What is the equation of the new graph? Choose 1 answer: (A) y=|x-4|-9 (B) y=|x-9|+4 (C) y=|x-9|-4 (D) y=|x-4|+9

The graph of y=∣x∣ y=|x| is shifted down by 99 units and to the right by 44 units.\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=∣x−4∣−9 y=|x-4|-9 \newline(B) y=∣x−9∣+4 y=|x-9|+4 \newline(C) y=∣x−9∣−4 y=|x-9|-4 \newline(D) y=∣x−4∣+9 y=|x-4|+9

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Full solution

Q. The graph of y=∣x∣ y=|x| is shifted down by 99 units and to the right by 44 units.\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=∣x−4∣−9 y=|x-4|-9 \newline(B) y=∣x−9∣+4 y=|x-9|+4 \newline(C) y=∣x−9∣−4 y=|x-9|-4 \newline(D) y=∣x−4∣+9 y=|x-4|+9
  1. Understanding shifts in equations: To determine the equation of the transformed graph, we need to understand how shifts affect the equation of a function. A shift to the right by hh units will replace xx with x−hx-h in the function's equation. A shift down by kk units will subtract kk from the function's value.
  2. Shifting the graph to the right: Since the original function is y=∣x∣y = |x|, shifting the graph to the right by 44 units will replace 'xx' with 'x−4x-4'. This gives us the intermediate function y=∣x−4∣y = |x-4|.
  3. Shifting the graph down: Next, shifting the graph down by 99 units will subtract 99 from the value of the function. This modifies our intermediate function to y=∣x−4∣−9y = |x-4| - 9.
  4. Comparing and choosing the correct equation: Now we compare our result with the given choices to find the correct equation. The equation y=∣x−4∣−9y = |x-4| - 9 matches choice (A).

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