Question

write a rule for $g$.
let the graph of $g$ be a vertical stretch by a factor of 3, followed by a translation 6 units left and 3 units up of the graph of $f(x)=e^{x}$.
$g(x)=\square$

Explanation:

Step1: Apply vertical stretch by 3

$3f(x) = 3e^x$

Step2: Translate 6 units left

$3f(x+6) = 3e^{x+6}$

Step3: Translate 3 units up

$3f(x+6) + 3 = 3e^{x+6} + 3$

Answer:

$g(x)=3e^{x+6}+3$