Math Problem Statement
Solution
The text in the image is written in Indonesian and can be translated as follows:
"The function is shifted 6 units to the right. The equation of the new function after the translation is:"
Given the information:
- The original function is .
- The function is shifted 6 units to the right.
To find the new function after a horizontal shift, we use the transformation rule for functions:
Where is the horizontal shift. If the shift is to the right, is positive. So, in this case, the new function after shifting 6 units to the right is:
So, the equation of the new function is:
Would you like more details on this or have any questions?
Here are some related questions:
- What is the effect of shifting a function vertically versus horizontally?
- How does the base of the exponential function affect its graph?
- What happens to the graph of if it is shifted to the left instead?
- How would the function change if instead of shifting, it was reflected over the x-axis?
- Can you generalize how to transform any function given different types of shifts and reflections?
Tip: When shifting functions horizontally, remember that moving to the right involves subtracting from the input variable, and moving to the left involves adding to it.
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Math Problem Analysis
Mathematical Concepts
Functions
Exponential Functions
Function Transformation
Formulas
F(x - h) = f(x) shifted h units to the right
Exponential Function: F(x) = a^x
Theorems
Transformation of Functions
Suitable Grade Level
Grades 9-12
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