Math Problem Statement
Solution
The image contains a table showing the equations of transformations applied to functions, including horizontal and vertical stretches (hsf and vsf) and their corresponding mapping notations. Let's break it down:
1. First row:
- Function:
- Stretch:
- hsf = 2 (horizontal stretch factor)
- vsf = 3 (vertical stretch factor)
- Mapping notation:
2. Second row:
- Function:
- Stretch:
- hsf = 3
- vsf =
- Mapping notation:
3. Third row:
- Function:
- Stretch:
- hsf =
- vsf =
- Mapping notation:
4. Fourth row:
- Function:
- Stretch:
- hsf =
- vsf =
- Mapping notation:
Would you like further clarification or details on how to apply these transformations?
Here are five related questions to deepen your understanding:
- How do you determine whether a function is being horizontally stretched or compressed?
- What effect does a vertical stretch factor greater than 1 have on the graph of a function?
- How would you describe the difference between a horizontal stretch and a reflection across the y-axis?
- What happens to the graph of a function when both horizontal and vertical transformations are applied?
- Can you apply a horizontal stretch and a translation to a function at the same time?
Tip: Horizontal transformations affect the x-coordinate inversely; for example, a factor of horizontally stretches by 2!
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Math Problem Analysis
Mathematical Concepts
Function Transformations
Horizontal Stretch
Vertical Stretch
Mapping Notation
Formulas
Horizontal stretch: y = f(c*x) -> x' = x/c
Vertical stretch: y = k*f(x) -> y' = k*y
Theorems
Function Transformations
Suitable Grade Level
Grades 9-12
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