Which set of steps will translate f (x) = 6x to g (x) = 6x - 5 - 7?

A.) Shift f (x) = 6x five units to the left and seven units up.

B.) Shift f (x) = 6x five units to the right and seven units down.

C.) Shift f (x) = 6x seven units to the right and five units up.

D.) Shift f (x) = 6x seven units to the left and five units down.

I think you missed to write the parenthesis because none of the choices are matching with answer.

Correct equation will be g (x) = 6 (x-5) - 7

to get g (x), first f (x) = 6x will chane to 6 (x-5).

Notice that here (x) changed to (x-5), when some number is subtracted from x then it shifts graph to the right.

hence 6 (x-5) will cause right side movement by 5 unit.

After that 6 (x-5) changes to 6 (x-5) - 7

when some number is subtracted at the end then that causes down movement.

so the graph will shift 7 unit down.

So finally we can say that choice "B.) Shift f (x) = 6x five units to the right and seven units down." is correct.