Math Problem Statement
Describe how the graph of g(x) is related to the graph of the parent function.
g(x)=−3|x|
Solution
The function is a transformation of the parent function , the absolute value function. Here's how the graph of relates to the parent function:
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Reflection: The negative sign in front of reflects the graph across the x-axis. Instead of opening upwards like , opens downwards.
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Vertical Stretch: The coefficient in causes a vertical stretch by a factor of 3. This means that for each -value, is 3 times as far from the x-axis compared to , making it steeper.
In summary, the graph of is a reflected and vertically stretched version of the parent function , opening downward with a steeper slope.
Would you like more details or have any questions?
- How would the graph change if the coefficient was -2 instead of -3?
- What if the coefficient was positive but greater than 1, like ?
- How does the graph change if the absolute value term includes a horizontal shift, such as ?
- How would a vertical shift affect ?
- What is the effect of adding a constant outside the absolute value, like ?
Tip: Transformations can be applied in sequence, and understanding each transformation's effect can make analyzing complex functions easier.
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Math Problem Analysis
Mathematical Concepts
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Formulas
g(x) = a|x| where 'a' affects vertical stretches and reflections
Theorems
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Suitable Grade Level
Grades 9-10