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The graph of y=|x| is shifted up by 7 units and to the left by 8 units. What is the equation of the new graph? Choose 1 answer: (A) y=|x+8|-7 (B) y=|x+8|+7 (C) y=|x-8|+7 (D) y=|x-8|-7

The graph of y=∣x∣ y=|x| is shifted up by 77 units and to the left by 88 units.\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=∣x+8∣−7 y=|x+8|-7 \newline(B) y=∣x+8∣+7 y=|x+8|+7 \newline(C) y=∣x−8∣+7 y=|x-8|+7 \newline(D) y=∣x−8∣−7 y=|x-8|-7

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Full solution

Q. The graph of y=∣x∣ y=|x| is shifted up by 77 units and to the left by 88 units.\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=∣x+8∣−7 y=|x+8|-7 \newline(B) y=∣x+8∣+7 y=|x+8|+7 \newline(C) y=∣x−8∣+7 y=|x-8|+7 \newline(D) y=∣x−8∣−7 y=|x-8|-7
  1. Understanding Shifts: To determine the equation of the transformed graph, we need to understand how shifts affect the equation of a function. A vertical shift up by 77 units adds 77 to the value of the function. A horizontal shift to the left by 88 units means we add 88 to the xx-value inside the function before applying the absolute value.
  2. Applying Horizontal Shift: Let's apply the horizontal shift first. Shifting the graph to the left by 88 units means we replace xx with (x+8)(x+8) in the absolute value function. The new function becomes y=∣x+8∣y = |x+8|.
  3. Applying Vertical Shift: Now, we apply the vertical shift. Shifting the graph up by 77 units means we add 77 to the entire function. So, the new function after both shifts is y=∣x+8∣+7y = |x+8| + 7.
  4. Matching the Result: We can now match our result with the given choices. The correct equation after applying both shifts is y=∣x+8∣+7y = |x+8| + 7, which corresponds to choice (B).

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