f(x - n) - shift the graph n units right
f(x + n) - shift the graph n units left
f(x) - n - shift the graph n units down
f(x) + n - shift the graph n units up ----------------------------------------------------------------------------
[tex]y=2(3)^x\\\\y=2(3)^{x-1}+4[/tex]
Answer: shift the graph of y = 2(3)ˣ one unit right and four units up.
The rule of translation is:
We know that if the function f(x) is translated k units to the right or left by k units if:
f(x) → f(x+k)
if k>0 then it is shifted k units to the left
and if k<0 then it is shifted k units to the right.
Also, the translation:
f(x) →f(x)+k
is a translation k units upward if k>0
and k units downward if k<0
The parent function is given by:
[tex]y=2\cdot 3^x[/tex]
The translated function:
[tex]y=2\cdot 3^{x-1}+4[/tex]
is a translation of the parent function 1 units to the right and 4 units upwards.
