Question

Find the function that is finally graphed after the following transformations are applied to the graph of y=/x in the order listed. ​(1) Reflect about the x-axis ​(2) Shift up 2 units ​(3) Shift right 4 units

Answer 1

The transformed function can be written as g(x) = -1/(x - 4) + 2

How to find the function:

We want to find the equation for:

y = 1/x = f(x)

When:

​(1) Reflect about the x-axis ​(2) Shift up 2 units ​(3) Shift right 4 units

First, a reflect about the x-axis just means that we need to multiply by -1, then:

g(x) = -f(x)

A shift up of 2 units means that we need to add 2.

g(x) = -f(x) + 2

A shift right of 4 units means that we need to subtract 4 i the argument:

g(x) = -f(x - 4) + 2

Then we can write:

g(x) = -1/(x - 4) + 2