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The graph of y=|x| is scaled vertically by a factor of (1)/(5). What is the equation of the new graph? Choose 1 answer: (A) y=(1)/(5)|x| (B) y=-5|x| (C) y=|x+5| (D) y=|x-5|

The graph of y=∣x∣ y=|x| is scaled vertically by a factor of 15 \frac{1}{5} .\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=15∣x∣ y=\frac{1}{5}|x| \newline(B) y=−5∣x∣ y=-5|x| \newline(C) y=∣x+5∣ y=|x+5| \newline(D) y=∣x−5∣ y=|x-5|

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Full solution

Q. The graph of y=∣x∣ y=|x| is scaled vertically by a factor of 15 \frac{1}{5} .\newlineWhat is the equation of the new graph?\newlineChoose 11 answer:\newline(A) y=15∣x∣ y=\frac{1}{5}|x| \newline(B) y=−5∣x∣ y=-5|x| \newline(C) y=∣x+5∣ y=|x+5| \newline(D) y=∣x−5∣ y=|x-5|
  1. Understanding vertical scaling: To determine the equation of the new graph, we need to understand what it means to scale a graph vertically by a factor of (1)/(5)(1)/(5). Scaling a graph vertically by a factor of (1)/(5)(1)/(5) means that every yy-value of the original graph is multiplied by (1)/(5)(1)/(5).
  2. Scaling the original equation: The original equation is y=∣x∣y = |x|. To scale this graph vertically by a factor of (1)/(5)(1)/(5), we multiply the entire right-hand side of the equation by (1)/(5)(1)/(5). This gives us the new equation y=15∣x∣y = \frac{1}{5}|x|.
  3. Checking the answer choices: Now we need to check the answer choices to see which one matches our new equation. The correct answer choice should be y=15∣x∣y = \frac{1}{5}|x|.
  4. Matching the new equation: Looking at the answer choices, we see that choice (A) y=15∣x∣y = \frac{1}{5}|x| matches the equation we derived for the new graph.

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