what is the equation of the graph of y=1/x if it is shifted 3 units to the right and 2 units down

Answer 1

y = (1/x-3) - 2

If it is shifted to the right then it should look like (x-3) if it is shifted to the left then it should look like (x+3)

If it is shifted up then it would look like [(1/x-3) + 2]. If it is shifted down then it would look like [(1/x-3) - 2]

Answer 2

When you shift the graph to the left or right, you directly change the x term. When you shift left, you add the number of units, and when you shift right, you subtract. Easy way to remember is that it's opposite from what you might think.

So to shift y = 1/x to the right by 3 units, you replace x with x - 3

y = 1 / (x-3)

I'm shifting 3 units to the right which means I only change the x term and I subtract to move rightwards (opposite of what seems intuitive).

To shift upwards and downwards, you change the y value. The same thinking applies. Move opposite of what you think is correct.

So to shift y = 1 / (x-3) down by 3 units, you replace y with with y + 2

y + 2 = 1 / (x-3)

Then you subtract 2 from both sides to make your equation into the form of y = f(x).

So,

y = (1 / (x-3)) - 2