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

Answer:

$y=\frac{0.25}{x-4}+3$

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:

$y=0.25 * \frac{1}{x} \\y=\frac{0.25}{x}$

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

$y=\frac{0.25}{x-4}$

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

$y=\frac{0.25}{x-4}+3$