Math Problem Statement
Solution
To solve this question:
Problem Breakdown
We start with the given function:
We are tasked with translating the function 3 units to the right and 5 units upwards.
Transformation Rules:
-
Rightward translation: To shift a function units to the right, replace with . For this case, , so replace with .
-
Upward translation: To shift a function units upwards, add to the entire function. For this case, , so add 5:
Simplify:
Correct Answer:
The correct choice is d. .
Would you like more explanation, or do you have further questions?
Related Questions:
- How do translations affect the vertex of a parabola?
- What happens when you translate a function to the left instead of right?
- How does a downward translation differ in terms of the equation?
- How can you identify the new vertex of a translated function?
- Can you rewrite this function in vertex form after translation?
Tip:
Always remember that translating a function horizontally involves modifying the -variable directly, while vertical translations add or subtract from the function itself.
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Math Problem Analysis
Mathematical Concepts
Function Transformation
Horizontal and Vertical Translations
Quadratic Functions
Formulas
f(x) = x^2 + 4
Translation Rule for Horizontal Shifts: f(x) → f(x - h)
Translation Rule for Vertical Shifts: f(x) → f(x) + k
Theorems
Translation Theorem for Functions
Suitable Grade Level
Grades 8-10
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