Question

What is the equation that moves g(x) = log2 x down 3 units?

Answer 1

When we want to translate the function to the right or left, we add a constant to its argument.

$f(x)\rightarrow f(x+a)$

If a is positive the function goes to the left, and if a is negative the function goes to the right.

When we want to translate the function up or down, we add a costant to the function value

$f(x)\rightarrow f(x)+a$

If a is positive, the function goes up, and if a is negative the function goes down.

Since we want to translate our function 3 units down, we need to subtract 3 from the original function

$g(x)\rightarrow g(x)-3$

Since our original function is

$g(x)=\log _2x$

The translated function is

$h(x)=\log _2x-3$