Question

Write a formula for the function g(x) obtained when the graph of f(x) = 1/x is shifted down 4 units and to the right 6 units .

Answer 1

Answer:  $g(x) = \frac{1}{x-6} - 4$

This can be written out as g(x) = 1/(x-6) - 4

The "x-6" is in the denominator, while the "-4" is not.

=============================================================

Explanation:

We'll start with the parent function $f(x) = \frac{1}{x}$

When we shift 4 units down, we're subtracting 4 from the y coordinate of each point on the curve. Which is the same as subtracting 4 from f(x) because y = f(x).

So we have $h(x) = f(x) - 4 = \frac{1}{x} - 4$ as an intermediate step.

Then to shift 6 units to the right, we'll replace every x with "x-6". Imagine we kept the h(x) curve completely still, and instead we moved the xy axis 6 units to the left. This would give the illusion of h(x) moving 6 units to the right if we made the xy axis stay still. So that's why we go for "x-6" instead of "x+6".

Therefore, we end up with $g(x) = \frac{1}{x-6} - 4$

Side note: plugging in x = 6 leads to a division by zero error. This would mean x = 6 is not in the domain.