Math Problem Statement
Solution
The image shows a problem in Indonesian that asks to determine the transformation of the function when it is shifted 2 units to the right and 1 unit up.
The general form for shifting a function is as follows:
- Shifting horizontally by units: (to the right) or (to the left).
- Shifting vertically by units: (up) or (down).
Given:
- The function is .
- A shift 2 units to the right means replacing with , so the horizontal transformation becomes .
- A shift 1 unit up means adding 1 to the function, making the vertical transformation .
Thus, the transformed function is:
This represents the function , shifted 2 units to the right and 1 unit up.
Would you like more details, or do you have any questions?
Here are 5 related questions to practice with:
- What is the transformation of if it is shifted 3 units to the left and 4 units down?
- How would you write the function if shifted 5 units to the right and 2 units down?
- If the function is reflected over the x-axis and then shifted 2 units up, what is the resulting equation?
- What happens to the graph of if it is shifted 1 unit to the right and stretched vertically by a factor of 3?
- How do you shift the graph of by 2 units left and 3 units up?
Tip: Always apply horizontal transformations before vertical ones when writing shifted functions.
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Math Problem Analysis
Mathematical Concepts
Function Transformations
Quadratic Functions
Formulas
Horizontal shift: f(x - h)
Vertical shift: f(x) + k
Theorems
Transformation of Functions
Suitable Grade Level
Grades 9-10
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