Math Problem Statement
Solution
The problem asks you to find the new function when the function is translated 1 unit to the left and 2 units up.
Translation steps:
- Left 1 unit: When you translate a function to the left, you add to the -value inside the absolute value. This means the transformation for shifting left 1 unit is .
- Up 2 units: When you translate a function up, you add to the entire function. So, adding 2 to the function results in .
Thus, the translated function .
The correct answer is:
- (Option B)
Would you like further details on transformations?
Here are some follow-up questions:
- What is the effect of shifting the function to the right instead of the left?
- How do you translate a function down instead of up?
- How do reflections affect the graph of an absolute value function?
- What happens when you multiply the absolute value function by a negative number?
- How does scaling the function vertically affect its shape?
Tip: Always remember, horizontal translations affect the -values, while vertical translations affect the entire function.
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Math Problem Analysis
Mathematical Concepts
Function Transformation
Absolute Value
Formulas
g(x) = f(x + h) + k
Theorems
Function Translation Theorem
Suitable Grade Level
Grades 9-12
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