Math Problem Statement
The following transformation were done to f(x)=x^3: right by 7 and flipped over x-axis
Solution
Given the function , we need to apply two transformations:
-
Shift the function to the right by 7 units.
To achieve this, we replace with . So the transformed function becomes:
-
Flip the function over the x-axis.
To flip a function over the x-axis, we multiply the entire function by . Thus, the final transformation becomes:
So, the transformed function is:
Do you want more details or have any questions?
Here are 5 related questions:
- What happens when a function is shifted left instead of right?
- How does a vertical flip affect the graph of different types of functions?
- What is the effect of flipping a function over the y-axis?
- How would the graph of change if we reflected it over both the x-axis and y-axis?
- How does horizontal scaling affect transformations?
Tip: For horizontal shifts, replacing with moves the graph right by units. Replacing it with moves the graph left.
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Math Problem Analysis
Mathematical Concepts
Function Transformations
Cubic Functions
Formulas
Horizontal shift: f(x - h) moves the graph h units right
Vertical flip: -f(x) reflects the graph over the x-axis
Theorems
Transformation Theorem
Suitable Grade Level
Grades 9-12
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