6. Example: Describe the sequence of transformations that will produce the graph of g(x) from the graph of f(x) when f(x) Ixl and g(x) = -3|2x + 4| – 5 Answer: 1. A horizontal compression by a factor of ½ 2. A horizontal translation (shift) 4 units to the left. 3. A vertical stretch by a factor of 3 4. A reflection across the x-axis 5. A vertical translation (shift) 5 units down. Now that you have seen this example. Describe the sequence of transformations that will produce the graph of g(x) from the -5(x - 2)2 + 8 %3D granh of f(x) when f(x) and g(x)
6. Example: Describe the sequence of transformations that will produce the graph of g(x) from the graph of f(x) when f(x) Ixl and g(x) = -3|2x + 4| – 5 Answer: 1. A horizontal compression by a factor of ½ 2. A horizontal translation (shift) 4 units to the left. 3. A vertical stretch by a factor of 3 4. A reflection across the x-axis 5. A vertical translation (shift) 5 units down. Now that you have seen this example. Describe the sequence of transformations that will produce the graph of g(x) from the -5(x - 2)2 + 8 %3D granh of f(x) when f(x) and g(x)
Transcribed Image Text:# Transformations of Functions
## Example Problem
**Example:** Describe the sequence of transformations that will produce the graph of \( g(x) \) from the graph of \( f(x) \) when \( f(x) = |x| \) and \( g(x) = -3|2x + 4| - 5 \).
**Answer:**
1. A horizontal compression by a factor of \( \frac{1}{2} \).
2. A horizontal translation (shift) 4 units to the left.
3. A vertical stretch by a factor of 3.
4. A reflection across the x-axis.
5. A vertical translation (shift) 5 units down.
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**Now that you have seen this example...**
Describe the sequence of transformations that will produce the graph of \( g(x) \) from the graph of \( f(x) \) when \( f(x) = x^2 \) and \( g(x) = -5(x - 2)^2 + 8 \).
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## Practice Problem
7. Suppose \( f(x) = x^3 \). Write a function \( g(x) \) whose graph can be obtained by translating the graph of \( f(x) \) 7 units to the left, stretching the graph of \( f(x) \) vertically by a factor of 3, reflecting the graph of \( f(x) \) across the x-axis, and translating the graph of \( f(x) \) 2 units down.
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