Question
Translate each graph as specified below. (a) The graph of \( y=|x| \) is shown. Translate it to get the graph of \( y=|x-5| \) (b) The graph of \( y=|x| \) is shown. Translate it to get the graph of \( y=|x|+4 \).
Ask by Weaver Nunez. in the United States
Feb 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) Shift the graph of \( y = |x| \) 5 units to the right to get \( y = |x - 5| \).
(b) Shift the graph of \( y = |x| \) 4 units up to get \( y = |x| + 4 \).
Solution
(a) To get the graph of y = |x – 5|, shift the graph of y = |x| 5 units to the right. This moves the vertex from (0, 0) to (5, 0).
(b) To get the graph of y = |x| + 4, shift the graph of y = |x| 4 units upward. This moves the vertex from (0, 0) to (0, 4).
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Simplify this solution The Deep Dive
To translate the graph of \( y=|x| \) to obtain the graph of \( y=|x-5| \), you shift the graph 5 units to the right along the x-axis. This is because the expression inside the absolute value, \( x-5 \), indicates that every x-value of the original graph is increased by 5. For the graph of \( y=|x|+4 \), you move the original graph of \( y=|x| \) upwards by 4 units along the y-axis. Here, the "+4" outside the absolute value indicates that every y-value of the original graph is increased by 4, creating a vertical shift.
