Answer:
[tex]y=\frac{0.25}{x-4}+3[/tex]
Step-by-step explanation:
Notice that we are requested to perform three transformations in order: first a vertical compression (of the variable "y"), second a horizontal shift (affecting therefore the horizontal variable "x"), and lastly a vertical translation (affecting the variable "y")
1) Recall that a vertical compression by a factor 0.25 involves multiplying the full function y(x) by the factor 0.25:
[tex]y=0.25 * \frac{1}{x} \\y=\frac{0.25}{x}[/tex]
2) the horizontal translation of 4 units to the right involves subtracting 4 from the variable "x":
[tex]y=\frac{0.25}{x-4}[/tex]
3) the vertical translation 3 units up involves adding 3 to the full expression for "y":
[tex]y=\frac{0.25}{x-4}+3[/tex]
