QQuestionMathematics
QuestionMathematics
Describe the transformation that involves a vertical stretch by a factor of 3 and a horizontal stretch by a factor of 1.
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Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Transformation
A transformation involves changing the shape, size, or position of a graph. In this case, we have two specific stretches: - Vertical stretch by a factor of 3 - Horizontal stretch by a factor of 1
Step 3:: Analyze the Vertical Stretch
- The general form of a vertical stretch is $$f(x) \rightarrow 3f(x)
- A vertical stretch by a factor of 3 means that every y-coordinate is multiplied by 3 - This will make the graph taller, expanding it vertically
Step 4:: Analyze the Horizontal Stretch
- The general form of a horizontal stretch is $$f(x) \rightarrow f(x/1)
- A horizontal stretch by a factor of 1 means no horizontal change occurs - Since the factor is 1, the graph remains unchanged horizontally
Step 5:: Combine the Transformations
- The vertical stretch will elongate the graph vertically by a factor of 3 - The horizontal stretch has no effect due to the factor of 1
Final Answer
The graph becomes 3 times taller but maintains its original horizontal width.
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