Math Problem Statement
Solution
The question in your image asks to fill in the blanks to correctly complete the following sentence:
"To obtain the graph of , shift the graph of to the left __ units and down __ units."
Explanation:
The function is a transformation of the basic cubic function .
- Horizontal shift: The term indicates a horizontal shift. Since it's , this means the graph shifts 8 units to the left (opposite of the sign).
- Vertical shift: The term outside the cubic function indicates a vertical shift downward by 2 units.
Conclusion:
- Left shift: 8 units
- Downward shift: 2 units
So, the answer should be:
- Shift to the left 8 units
- Shift down 2 units
Would you like more details or have any other questions?
5 Related Questions:
- How do you shift other types of functions horizontally or vertically?
- What happens if the transformation inside the parentheses was ?
- How does the general transformation of affect graphs?
- What is the effect of a reflection on the graph of ?
- How do horizontal stretches and compressions affect the graph of a cubic function?
Tip:
When analyzing transformations, always pay attention to the signs inside and outside the parentheses to determine the direction of shifts or reflections!
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Math Problem Analysis
Mathematical Concepts
Algebra
Function Transformations
Cubic Functions
Formulas
f(x) = (x + h)^3 + k
Theorems
Transformation Theorem
Horizontal and Vertical Shifts
Suitable Grade Level
Grades 9-12
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