Question

Write the equation of the graph obtained when the graph of y=1/x is compressed vertically by a factor of 0.25, translated 4 units right, and then translated 3 units up.

Answer 1

`y=(0.25)/(x-4)+3`

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:

`y=0.25 * (1)/(x) \\y=(0.25)/(x)`

2) the horizontal translation of 4 units to the right involves subtracting 4 from the variable "x":

`y=(0.25)/(x-4)`

3) the vertical translation 3 units up involves adding 3 to the full expression for "y":

`y=(0.25)/(x-4)+3`