Math Problem Statement
The point A(-3, 2) lies on the graph with equation y = f(x). If the graph of the related function y = -f(x) + 3 is drawn, what will the image of A be?
Solution
The problem gives us the point on the graph of and asks for the image of when the graph is transformed to .
Step-by-step approach:
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Given Information:
- lies on the graph of , meaning .
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Transformation: The transformation is .
- The term reflects the graph over the x-axis.
- The term shifts the graph vertically by 3 units upwards.
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Apply the transformation to the point:
- Start with .
- For the new function, :
Thus, the image of point under the transformation is .
Conclusion:
The image of will be .
Let me know if you'd like further details or have any questions!
Related questions:
- What is the effect of the transformation on the graph?
- How does a vertical shift affect the coordinates of a point on a graph?
- What happens to the graph when a negative sign is applied to a function?
- How can we generalize transformations for any point ?
- Can you explain what a horizontal reflection would look like?
Tip:
Whenever dealing with transformations, always consider how the reflection (negative sign) and shifts affect each point individually.
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Math Problem Analysis
Mathematical Concepts
Function Transformation
Coordinate Geometry
Formulas
y = -f(x) + 3
Theorems
Function Reflection and Vertical Shift
Suitable Grade Level
Grades 10-12