Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To identify the type of transformation and describe the change from the function [tex]\( f(x) = \log x \)[/tex] to [tex]\( g(x) = \log(x) - 3 \)[/tex], let's break down the steps in detail:
1. Understand the Original Function:
The original function is [tex]\( f(x) = \log x \)[/tex]. This is a logarithmic function, which typically has its graph passing through the point (1,0) and increases slowly as [tex]\( x \)[/tex] increases.
2. Identify the Transformed Function:
The transformed function is [tex]\( g(x) = \log(x) - 3 \)[/tex]. This function is derived from [tex]\( f(x) \)[/tex] by subtracting 3 from [tex]\( \log x \)[/tex].
3. Determine the Type of Transformation:
When a constant is subtracted from the entire function [tex]\( f(x) \)[/tex], it results in a vertical shift. Specifically, subtracting 3 means that every point on the graph of [tex]\( f(x) \)[/tex] is moved down by 3 units.
4. Describe the Change:
For the given transformation, [tex]\( g(x) = \log(x) - 3 \)[/tex] indicates that the graph of [tex]\( f(x) = \log x \)[/tex] is shifted vertically downward by 3 units. Thus, every [tex]\( y \)[/tex]-value of the original function [tex]\( f(x) \)[/tex] is decreased by 3.
Conclusion:
The transformation from [tex]\( f(x) = \log x \)[/tex] to [tex]\( g(x) = \log(x) - 3 \)[/tex] is a vertical shift. Specifically, the graph of [tex]\( f(x) \)[/tex] is shifted 3 units downward to produce [tex]\( g(x) \)[/tex].
So, the type of transformation is:
- Vertical shift
And the description of the change is:
- The graph of [tex]\( f(x) = \log x \)[/tex] is shifted 3 units downward to get [tex]\( g(x) = \log(x) - 3 \)[/tex].
This completes the detailed explanation of identifying and describing the transformation.
1. Understand the Original Function:
The original function is [tex]\( f(x) = \log x \)[/tex]. This is a logarithmic function, which typically has its graph passing through the point (1,0) and increases slowly as [tex]\( x \)[/tex] increases.
2. Identify the Transformed Function:
The transformed function is [tex]\( g(x) = \log(x) - 3 \)[/tex]. This function is derived from [tex]\( f(x) \)[/tex] by subtracting 3 from [tex]\( \log x \)[/tex].
3. Determine the Type of Transformation:
When a constant is subtracted from the entire function [tex]\( f(x) \)[/tex], it results in a vertical shift. Specifically, subtracting 3 means that every point on the graph of [tex]\( f(x) \)[/tex] is moved down by 3 units.
4. Describe the Change:
For the given transformation, [tex]\( g(x) = \log(x) - 3 \)[/tex] indicates that the graph of [tex]\( f(x) = \log x \)[/tex] is shifted vertically downward by 3 units. Thus, every [tex]\( y \)[/tex]-value of the original function [tex]\( f(x) \)[/tex] is decreased by 3.
Conclusion:
The transformation from [tex]\( f(x) = \log x \)[/tex] to [tex]\( g(x) = \log(x) - 3 \)[/tex] is a vertical shift. Specifically, the graph of [tex]\( f(x) \)[/tex] is shifted 3 units downward to produce [tex]\( g(x) \)[/tex].
So, the type of transformation is:
- Vertical shift
And the description of the change is:
- The graph of [tex]\( f(x) = \log x \)[/tex] is shifted 3 units downward to get [tex]\( g(x) = \log(x) - 3 \)[/tex].
This completes the detailed explanation of identifying and describing the transformation.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.