Respuesta :
General Idea:
In general for the function of the form [tex] f(x) = ag(x+c) [/tex], c represents the horizontal translation to the left, for [tex] a > 1 [/tex], ' a ' represents vertically stretch by factor of ' a ', and for [tex] 0 < a < 1 [/tex], ' a' represents vertical compression by factor of ' a '.
Application of Concept:
Here in our problem, [tex] f(x) = 5e^{x+3} [/tex] and [tex] g(x)=e^x [/tex].
We can rewrite our function as [tex] f(x) =5g(x+3) [/tex]
In our problem a = 5 and c = 3.
Conclusion:
The description of graph of [tex] f(x) = 5e^{x+3} [/tex] as transformation of the graph of [tex] g(x)=e^x [/tex] will be "A vertical stretch of 5 and a horizontal translation 3 units to the left"
