To match each transformation of [tex]\( f(x) = |x| \)[/tex] with the correct description, let's analyze each given transformation one by one:
1. Transformation: [tex]\( g(x) = |4x| \)[/tex]
- Description: Horizontal compression by a factor of 4.
- This occurs because multiplying the input [tex]\( x \)[/tex] by a factor greater than 1 results in a horizontal compression of the graph.
2. Transformation: [tex]\( g(x)=\frac{1}{10}|x| \)[/tex]
- Description: Vertical compression by a factor of 10.
- This occurs because multiplying the output of [tex]\( f(x) \)[/tex] by a fraction less than 1 results in a vertical compression of the graph.
3. Transformation: [tex]\( g(x)=|1/4x| \)[/tex]
- Description: Horizontal stretch by a factor of 4.
- This occurs because multiplying the input [tex]\( x \)[/tex] by a fraction less than 1 results in a horizontal stretch of the graph.
4. Transformation: [tex]\( g(x)=10|x| \)[/tex]
- Description: Vertical stretch by a factor of 10.
- This occurs because multiplying the output of [tex]\( f(x) \)[/tex] by a factor greater than 1 results in a vertical stretch of the graph.
To summarize the matches correctly:
- [tex]\( g(x) = |4x| \)[/tex] matches with Horizontal compression by a factor of 4.
- [tex]\( g(x)=\frac{1}{10}|x| \)[/tex] matches with Vertical compression by a factor of 10.
- [tex]\( g(x)=|1/4x| \)[/tex] matches with Horizontal stretch by a factor of 4.
- [tex]\( g(x)=10|x| \)[/tex] matches with Vertical stretch by a factor of 10.
