Reflection over the y-axis = change [tex]x\mapsto -x[/tex]
Compress by a factor of k = multiply by k
So, in your case, we first change the sign of the argument. Note that this has no effect, because f(x) is symmetric with respect to the y-axis:
[tex]|x|\mapsto |-x| = |x|[/tex]
Then, we compress the function, multiplying it by the scaling factor:
[tex]|x| \mapsto g(x)=\dfrac{|x|}{9}[/tex]
The reflection and the horizontal compressions are illustrations of transformations.
The formula for function g(x) is [tex]\mathbf{g(x) = 9x}[/tex]
The function is given as:
[tex]\mathbf{f(x) = |x|}[/tex]
The rule of reflection over the y-axis is:
[tex]\mathbf{(x,y) \to (-x,y)}[/tex]
So, we have:
[tex]\mathbf{f'(x) = |-x|}[/tex]
[tex]\mathbf{f'(x) = x}[/tex]
The rule of horizontal compression is:
[tex]\mathbf{(x,y) \to (\frac xb,y)}[/tex]
So, we have:
[tex]\mathbf{g(x) = \frac{x}{1/9}}[/tex]
[tex]\mathbf{g(x) = 9x}[/tex]
Hence, the formula for function g(x) is [tex]\mathbf{g(x) = 9x}[/tex]
Read more about transformations at:
https://brainly.com/question/11707700
