Math Problem Statement
Solution
To solve the problem of determining the equation for the transformed function when the original function is shifted left by 1 unit, we need to understand how horizontal shifts affect the function.
Transformation Explanation:
When a function is shifted to the left by units, the new function can be written as: In this case, since the function is shifted left by 1 unit, the transformed function will be: Substituting the original function into this, we get:
Final Answer:
The equation for the transformed function is:
Would you like to go into more details or have any questions?
Here are some related questions to explore further:
- What is the effect on the graph when the function is shifted right by 1 unit instead?
- How does shifting the function up or down affect the equation?
- What is the general formula for shifting a function horizontally by any number of units?
- How does the domain of change after the transformation?
- Can we apply multiple transformations to ? How would you describe the transformation if the function is shifted left by 1 and down by 2?
Tip: When shifting functions horizontally, the direction of the shift is opposite the sign inside the function's argument.
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Math Problem Analysis
Mathematical Concepts
Function Transformation
Square Root Function
Formulas
f(x + h) represents a horizontal shift by h units
Theorems
Function Transformation Theorem
Suitable Grade Level
Grades 9-10
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