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.

The equation is y = 0.25/(x - 4) + 3

Step-by-step explanation:

If we have a function y = f(x)

A compression means that we multiply the function by a factor smaller than 1.

Then the vertical compression by a factor of 0.25 is:

y = 0.25*f(x)

a translation by A units to the right, means that we need to valuate the function in x - A.

So now we have:

y = 0.25*f(x - 4)

A translation in the y-axis means that we need to add a constant to the equation, then if we tralate it by 3 units up, we have:

y = 0.25*f(x - A) + 3

Then, if f(x) = 1/x

Our new equation is:

y = 0.25/(x - 4) + 3

answer: (3,11) is your answer.