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Transformation of Graphs Video Lecture - Civil Engineering (CE)

FAQs on Transformation of Graphs Video Lecture - Civil Engineering (CE)

1. What is the transformation of graphs?
Ans. The transformation of graphs refers to the process of changing the position, shape, or size of a graph without altering its basic structure. This is achieved by applying various mathematical operations such as translations, reflections, stretches, and compressions.
2. How can translations affect the graph of a function?
Ans. Translations can shift the graph of a function horizontally or vertically. For example, a horizontal translation moves the graph left or right, while a vertical translation moves it up or down. These translations are determined by adding or subtracting values to the original function.
3. What is the impact of reflections on the graph of a function?
Ans. Reflections can change the orientation of a graph by flipping it across a specific axis. A reflection across the x-axis turns the graph upside down, while a reflection across the y-axis mirrors the graph horizontally. These reflections are obtained by negating the x or y values in the original function.
4. How do stretches and compressions affect the graph of a function?
Ans. Stretches and compressions alter the size of a graph. A stretch horizontally expands the graph, making it wider, while a compression horizontally shrinks it, making it narrower. Similarly, a vertical stretch or compression affects the height of the graph. These transformations are achieved through multiplication or division of the x or y values in the original function.
5. Can multiple transformations be applied to a graph simultaneously?
Ans. Yes, multiple transformations can be applied to a graph simultaneously. When multiple transformations are applied, they are performed in a specific order. This order can be remembered using the acronym "SHRINK": Stretch/Compress, Horizontal shift, Reflect, Increase/Decrease (vertical shift), and New graph. By following this order, the desired transformations can be accurately applied to the original graph.
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