write a rule for g of f(x)

Question

what is the rule for 4 units right and 1 unit down followed by a vertical shrink by a factor of 1/3 of the graph f(x)= e^-x

Answer 1

g(x) = (1/3)*exp(-x-4)-1

= (1/3) * 1/ exp(x+4) - 1

Answer 2

In general ±a•f(x ± h) ± k is how you transform any function. Putting a negative sign up front will flip it vertically. Multiplying by a number up front ("a") will stretch vertical when a > 1 and smoosh it down when 0 < a < 1. Add h shifts left (counterintuitive, I know). Subtract h shifts right. Add k shifts up (makes sense). Subtract k shifts down. Therefore...

g(x) = 1/3•e^x-4 - 1