Math Problem Statement
describe the transformations from the parent graph g(x)=-square root of x-3+2
Solution
The given function is . To describe the transformations from the parent graph , we break down the changes step by step:
-
Horizontal Translation (Right Shift):
- The term inside the square root, , indicates a horizontal shift.
- Since it's , the graph shifts 3 units to the right.
-
Reflection (Vertical Flip):
- The negative sign in front of the square root, , reflects the graph across the x-axis. This means the graph will now point downward instead of upward.
-
Vertical Translation (Up Shift):
- The outside the square root shifts the graph 2 units up.
Summary of Transformations:
- The parent graph is first shifted 3 units to the right.
- It is then reflected across the x-axis (flipped upside down).
- Finally, it is shifted 2 units up.
Would you like more details on any of these transformations?
5 Related Questions:
- How would the graph change if the function was ?
- What does a vertical stretch or compression look like in a square root function?
- How can you graph by hand?
- What effect does a horizontal reflection (over the y-axis) have on the square root function?
- How do horizontal translations differ from vertical translations in general?
Tip:
When analyzing transformations, always start with the operations inside the function (like shifts and reflections), then move to outside operations (like stretching and translations).
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Math Problem Analysis
Mathematical Concepts
Graph Transformations
Square Root Functions
Function Reflections
Translations
Formulas
g(x) = -√(x - 3) + 2
f(x) = √x
Theorems
Transformation of Functions Theorem
Suitable Grade Level
Grades 9-12
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