Answer: f(x) = ln(x + 5)
Explanation:
This type of functions that first are steep, and as x increases the steepness of the function decreases, are logarithmic functions.
Then we can write this in a general way as:
f(x) = a*Ln(x + b) + c
Where a, b, and c are constants.
Now we know that Ln(x) has an asymptote at x = 0.
And in our graph, the asymptote is at x = -5
Then we must have that: -5 + b = 0
b = 5.
Now we have f(x) = a*ln(x + 5) + c.
The only other information that we have is that, when x = 0, f(0) is a value between 1 and 2 (closer to 2 actually), then:
Ln(0 + 5) = ln(5) = 1.61
From this we can conclude that a = 1 and c = 0 (Really, a ≈ 1 and c ≈ 0, but we can not really find these values if we do not have more info, then we will assume that a equals 1 and c equals 0)
f(x) = ln(x + 5)