Math Problem Statement
The function f(x) = ∛x is translated 3 units in the negative y-direction and 8 units in the negative x-direction. Select the correct equation for the resulting function.
Solution
To determine the new function after translating :
-
Translation 3 units in the negative -direction:
- Moving downward by 3 units translates the function vertically. This affects the function by subtracting 3 from .
- So, .
-
Translation 8 units in the negative -direction:
- Moving left by 8 units translates the function horizontally. This affects the -term inside the function, changing to .
- So, .
Therefore, the resulting function is:
Answer:
The correct choice is:
- C)
Would you like a more detailed explanation of each translation?
Here are 5 related questions to further explore this topic:
- How does translating a function affect its graph?
- What happens if we translate a function in both positive - and -directions?
- How would a reflection over the -axis change the function ?
- How do we determine the transformations for different types of functions, such as quadratic or exponential functions?
- What are the differences between vertical and horizontal transformations?
Tip: When translating functions, remember that changes inside the function (like ) affect the -direction, while changes outside the function (like ) affect the -direction.
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Math Problem Analysis
Mathematical Concepts
Function Transformation
Translations
Cube Root Functions
Formulas
f(x) = ∛(x + h) + k, where h is the horizontal translation and k is the vertical translation
Theorems
Translation of functions theorem
Suitable Grade Level
Grades 9-11