Respuesta :
Given:
The linear parent function, f(x)=x is vertically compressed by a factor of 4 and reflected over the x-axis.
To find:
The new function.
Solution:
The vertical stretch and compression is defined as
[tex]g(x)=kf(x)[/tex]
If k>1, then f(x) vertically stretched by factor k and if 0<k<1, then f(x) vertically compresses by factor [tex]\dfrac{1}{k}[/tex].
In the given problem, linear parent function, f(x)=x is vertically compressed by a factor of 4. So, [tex]k=\dfrac{1}{4}.[/tex]
[tex]g(x)=\dfrac{1}{4}f(x)[/tex]
Then, it is reflected over the x-axis.
[tex]G(x)=-g(x)[/tex]
[tex]G(x)=-\dfrac{1}{4}f(x)[/tex] [tex][\because g(x)=\dfrac{1}{4}f(x)][/tex]
[tex]G(x)=-\dfrac{1}{4}x[/tex] [tex][\because f(x)=x][/tex]
So, the new function is [tex]G(x)=-\dfrac{1}{4}x[/tex].
Therefore, the correct option is B.
