Math Problem Statement
Solution
The graph provided shows the function , which is a basic parabola centered at the origin. You are asked to shift this graph 2 units to the right.
When shifting a function horizontally, the general transformation is:
Where is the horizontal shift. In this case, the shift is 2 units to the right, so the new function becomes:
Thus, after shifting the graph 2 units to the right, the transformed function is:
Would you like more details or explanations?
Here are five related questions you might find helpful:
- How would the function change if the shift was 3 units to the left instead?
- What happens if you apply a vertical shift instead of a horizontal one?
- How does the vertex of the parabola change with horizontal shifts?
- Can you describe how stretching or compressing affects the graph?
- What if we shift the graph vertically and horizontally simultaneously?
Tip: Remember, shifting right is done by subtracting a positive value from , while shifting left is done by adding a value.
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Math Problem Analysis
Mathematical Concepts
Functions
Quadratic Functions
Transformations
Formulas
f(x - h): Horizontal shift transformation for functions
Standard quadratic form: f(x) = x^2
Theorems
Transformation of functions
Suitable Grade Level
Grades 8-10
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