The graph of y=|x| is shifted up by 4 units and to the right by 5 units. What is the equation of the new graph? Choose 1 answer: (A) y=|x+4|-5 (B) y=|x+5|+4 (C) y=|x-5|+4 (D) y=|x+4|+5

Question

The graph of  y=|x| is shifted up by 4 units and to the right by 5 units. What is the equation of the new graph? Choose 1 answer: (A)  y=|x+4|-5 (B)  y=|x+5|+4 (C)  y=|x-5|+4 (D)  y=|x+4|+5

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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 4 units adds 4 to the value of y in the original equation. A horizontal shift to the right by 5 units subtracts 5 from the value of x in the original equation.Vertical shift up: The original equation is y = |x|. To shift the graph up by 4 units, we add 4 to the y-value, resulting in y = |x| + 4.Horizontal shift to the right: To shift the graph to the right by 5 units, we subtract 5 from the x-value inside the absolute value, resulting in y = |x - 5| + 4.Comparing transformed equation: Now we compare the transformed equation with the given choices to find the correct answer. (A) y = |x + 4| - 5 is incorrect because it represents a shift to the left by 4 units and down by 5 units. (B) y = |x + 5| + 4 is incorrect because it represents a shift to the left by 5 units and up by 4 units. (C) y = |x - 5| + 4 is correct because it represents a shift to the right by 5 units and up by 4 units. (D) y = |x + 4| + 5 is incorrect because it represents a shift to the left by 4 units and up by 5 units.

The graph of $y=|x|$ is shifted up by $4$ units and to the right by $5$ units. $\newline$ What is the equation of the new graph? $\newline$ Choose $1$ answer: $\newline$ (A) $y=|x+4|-5$ $\newline$ (B) $y=|x+5|+4$ $\newline$ (C) $y=|x-5|+4$ $\newline$ (D) $y=|x+4|+5$

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