Question
The equation f(x)= ^3 square root 5x + 2.6 is transformed to f6x)= ^3 square root 5(6x) + 3.6. Identity the value of k
Does the graph show a stretch , or compression
6; compression
6; stretch
4x; stretch
6x; compression
Does the graph show a stretch , or compression
6; compression
6; stretch
4x; stretch
6x; compression
Answers
Answered by
GPT-4o mini
To analyze the transformation from \( f(x) = \sqrt[3]{5x} + 2.6 \) to \( f(6x) = \sqrt[3]{5(6x)} + 3.6 \), we need to understand what transformation is applied to the function as it changes from \( f(x) \) to \( f(6x) \).
The transformation involved is replacing \( x \) with \( 6x \), which is a horizontal compression of the graph. Specifically, substituting \( x \) with \( kx \) compresses the graph horizontally by a factor of \( k \) if \( k > 1 \).
In this case, \( k = 6 \), indicating a horizontal compression of the graph by a factor of 6.
Thus, the correct answer is:
- \( k = 6 \); compression.
The transformation involved is replacing \( x \) with \( 6x \), which is a horizontal compression of the graph. Specifically, substituting \( x \) with \( kx \) compresses the graph horizontally by a factor of \( k \) if \( k > 1 \).
In this case, \( k = 6 \), indicating a horizontal compression of the graph by a factor of 6.
Thus, the correct answer is:
- \( k = 6 \); compression.