Math Problem Statement
Describe how the graph of g(x) is related to the graph of the parent function.
g(x)=||−2x||
vertical translation: 1 of 4. Select Choice
horizontal translation: 2 of 4. Select Choice
dilation: 3 of 4. Select Choice
reflection: 4 of 4. Select Choice
Solution
The function is a transformation of the parent function , which is the absolute value function.
Here's how the transformations apply:
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Reflection: Since there is a negative sign in front of the , it reflects the graph over the y-axis. However, because this function is within an absolute value (which negates the effect of a reflection over the y-axis), it does not actually change the shape visually on the positive or negative sides.
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Dilation: The factor in causes a horizontal compression. This means the graph of is "squeezed" horizontally by a factor of compared to . This makes it steeper than the original parent function.
So, the correct answer is dilation due to the factor of 2, which compresses the graph horizontally.
Would you like more details, or have any questions?
Here are 5 questions to further explore this topic:
- How does a positive constant multiplier affect the dilation of the absolute value function?
- What would happen if the function were ?
- How would adding a constant outside the absolute value affect the graph?
- If we applied a vertical reflection, how would that affect the graph of ?
- How would the graph change if we shifted horizontally?
Tip: When you see a constant multiplied by inside an absolute value function, it typically indicates a horizontal stretch or compression.
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Math Problem Analysis
Mathematical Concepts
Absolute Value Functions
Transformations
Reflection
Dilation
Formulas
g(x) = |−2x|
f(x) = |x|
Theorems
-
Suitable Grade Level
Grades 9-10