Math Problem Statement
Solution
The question provided is written in Persian and includes a mathematical expression. I'll translate and interpret it to guide you through the solution.
Translation:
- The problem gives the point on the graph of the function . It asks you to determine the coordinates of point on the graph of the function .
Step-by-Step Solution:
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Initial Function: The given function is , and point lies on this curve.
- This means that for , .
- So, we substitute and into the equation : Solving for : Therefore, .
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New Function: The next part of the problem asks for the coordinates on the graph of the transformed function .
- In this case, we have a horizontal shift of the function by 2 units to the right.
- We know , so now we are interested in the value of when .
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Finding : If , and we are now dealing with , we substitute (since ) into :
- For , .
Thus, the coordinates on the new graph of corresponding to point are .
Would you like more details or have any further questions?
Here are 5 related questions to extend this concept:
- What is the effect of a vertical shift on the graph of ?
- How do horizontal shifts affect the domain of a function?
- What happens to the graph of if you apply both vertical and horizontal shifts?
- Can we find the inverse of , and how does the graph change?
- What are the coordinates of point if the function is transformed to ?
Tip: Always check how transformations like horizontal shifts impact the input variable when applying them to functions.
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Math Problem Analysis
Mathematical Concepts
Function transformations
Graph shifts
Formulas
f(x - h) results in a horizontal shift by h units
y = 3 - f(x)
Theorems
Graph transformations
Horizontal and vertical shifts
Suitable Grade Level
Grades 10-12