Question
What value of k would create the function y=f(kx) on the graph if it is a transformed version of the function f(x)=x+2
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(1 point)
k=_
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(1 point)
k=_
Answers
GPT-4o mini
To create a transformed version of the function \( f(x) = x + 2 \) in the form \( y = f(kx) \), we need to determine the value of \( k \) that results in a horizontal scaling of the graph.
The effect of \( k \) on the function \( f(kx) \):
- If \( k > 1 \), the graph of the function will compress horizontally.
- If \( 0 < k < 1 \), the graph will stretch horizontally.
If you don't have a specific transformation (for example, compressing or stretching by a specific factor), you can choose a common value. A standard transformation is using \( k = 1 \), which would leave the function unchanged.
If you have a specific horizontal stretch or compression you want to achieve, please clarify. Otherwise, the most straightforward value for \( k \) to create a transformed version similar to \( f(x) = x + 2 \) without additional transformations could be:
\[ k = 1 \]
If you would like a different type of transformation, please specify, and I can provide that value for \( k \).
The effect of \( k \) on the function \( f(kx) \):
- If \( k > 1 \), the graph of the function will compress horizontally.
- If \( 0 < k < 1 \), the graph will stretch horizontally.
If you don't have a specific transformation (for example, compressing or stretching by a specific factor), you can choose a common value. A standard transformation is using \( k = 1 \), which would leave the function unchanged.
If you have a specific horizontal stretch or compression you want to achieve, please clarify. Otherwise, the most straightforward value for \( k \) to create a transformed version similar to \( f(x) = x + 2 \) without additional transformations could be:
\[ k = 1 \]
If you would like a different type of transformation, please specify, and I can provide that value for \( k \).