I know the property of Horizontal shrink is $y=f(cx)$ where $ c>1$ and we need to divide the $x$ coordinates by the factor.
Horizontal Stretch is $y=f(cx)$ where $0<c<1$ and we also need to divide the $x$ coordinates by the factor.
IHere I have a question i'm trying to find: $f(x)= -x+5$; horizontal shrink by a factor of $\frac{1}{2}$ The answer to that is $f(x)=-2x+5$.
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$\begingroup$Note: Horizontal Shrink $=$ Vertical Stretch
So, when they ask you to shrink the function horizontally by a factor of $\frac 12$, you can think of it as stretching the function by a factor of $2$. Using this, you can say that $f(x)=-x+5$, when horizontally shrunk/vertically stretched becomes $|-2x+5|$.
Also, the question:
What is new function after $f(x)=-x+5$ is horizontally shrunk by a factor of $\frac 12$?
is unclear. This is because shrunk by a factor of $\frac 12$ can also mean stretched by a factor of $2$. However, in most cases, horizontally shrunk by a factor of $\frac 12$ will mean the same thing as horizontally shrunk by a factor of $2$.
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