The equation  f(x)=2x−9f(x)=2x−9 translated 6  units up  is g(x)=

Start from

When you vertically translate the graph of a function, you are adding a constant to that equation, i.e. you're performing the transformation

You translate the function units up if and k units down if

So, in your case, you have to add 6 to the function:

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)