Write an equation for the transformed logarithm shown below

Write an equation for the transformed logarithm shown below, that passes through (- 2, 0) and (2, - 3) f(x) =

given graph has a vertical asymptote at x = -3

so the graph will have equation of form:

f(x) = -a*log (x + 3) + k

where a = vertical shift

k = vertical stretch

Now using the given point:

(-2, 0)

0 = -a*log (-2 + 3) + k

0 = -a*log 1 + k

k = 0

(2, -3)

-3 = -a*log (2 + 3) + 0

a = 3/log 5

So given function will be:

f(x) = [-3*log (x + 3)]/log 5