Math Problem Statement
Solution
The graph shows two functions, and , with represented by the blue curve and by the red curve. The task is to identify the transformation that converts into .
Key Observations:
- is the red curve, which appears to be a horizontal shift of (blue curve) to the right by 2 units.
This suggests that the transformation applied to to obtain is a horizontal shift to the right by 2 units. A horizontal shift to the right corresponds to the transformation:
Thus, the correct answer is:
Do you need further explanation or have any questions?
Here are 5 related questions to deepen your understanding:
- What happens when you shift a graph horizontally to the left by 3 units?
- How does a vertical shift differ from a horizontal shift in graph transformations?
- What transformation does represent?
- Can you describe how transforms the graph of ?
- What is the effect of the transformation on ?
Tip: Horizontal transformations affect the input (x-values), while vertical transformations affect the output (y-values).
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Math Problem Analysis
Mathematical Concepts
Functions
Transformations
Horizontal shifts
Formulas
g(x) = f(x - h) (horizontal shift by h units)
g(x) = f(x) + k (vertical shift by k units)
Theorems
Transformation of functions
Suitable Grade Level
Grades 9-11