Determine the function which corresponds to the given graph. (5 points) The asymptote is x = -5.

f(x) = ln(x + 5)

Step-by-step 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)

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