The expression that represents transformation is [tex]-f(\frac 12x)-4[/tex]
The equation of the function is given as:
[tex]f(x) = x[/tex]
The rule of horizontal stretch by a factor of 2 is represented as:
[tex](x,y) \to (\frac 12x,y)[/tex]
So, we have:
[tex]y = f(\frac 12x)[/tex]
The rule of reflection over the x-axis is represented as:
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex]y = -f(\frac 12x)[/tex]
The rule of a vertical shift down by 4 units is:
[tex](x,y) \to (x,y-4)[/tex]
So, we have:
[tex]y = -f(\frac 12x)-4[/tex]
Hence, the expression that represents transformation is [tex]-f(\frac 12x)-4[/tex]
Read more about function transformation at:
https://brainly.com/question/1548871
