Question
Which of the following describes graphing \( y \geq|x|+4 \) ? Translate \( y=|x| \) up 4 units and shade inside the \( V \). Translate \( y=|x| \) right 4 units and shade inside the \( V \). Translate \( y=|x| \) left 4 units and shade inside the \( V \). Translate \( y=|x| \) down 4 units and shade inside the \( V \).
Ask by Bowman Delgado. in the United States
Feb 26,2025
Upstudy AI Solution
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Answer
To graph \( y \geq |x| + 4 \), translate \( y = |x| \) up 4 units and shade inside the V.
Solution
To graph the inequality \( y \geq |x| + 4 \), we need to understand the graph of \( y = |x| \) and then apply the given translations.
1. The graph of \( y = |x| \) is a V-shaped graph with its vertex at the origin (0,0). The graph opens upwards.
2. To graph \( y \geq |x| + 4 \), we need to translate the graph of \( y = |x| \) up 4 units. This means that every point on the graph of \( y = |x| \) will be shifted 4 units upwards.
3. After translating the graph of \( y = |x| \) up 4 units, the new graph will be \( y = |x| + 4 \). This graph will also be a V-shaped graph, but it will be shifted upwards by 4 units.
Therefore, the correct description of graphing \( y \geq |x| + 4 \) is to translate \( y = |x| \) up 4 units and shade inside the V.
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Simplify this solution Mind Expander
To graph the inequality \( y \geq |x| + 4 \), you start with the basic V-shape of \( y = |x| \). By adding 4, you shift the entire graph of \( y = |x| \) up by 4 units. The "shading inside the V" indicates that the area above the graph (including the boundary line) is part of the solution since \( y \) is greater than or equal to the expression. After you've got that graph up 4 units, don't forget to draw a solid line for \( y = |x| + 4 \) because the inequality includes "equal to." The area above the graph represents all the points where \( y \) exceeds or equals the values of \( |x| + 4 \). Grab some colored pencils and get ready to showcase your artistic side while you shade!
