Question

Determine the function which corresponds to the given graph. a natural logarithmic function crossing the y axis at zero and going through the point 2,1.

The asymptote is x = -1.

Answer 1

check the picture below.

notice, is ln(x), but just shifted horizontally to the left by 2 units, thus (x + 2)

Answer 2

The function for the given description is y = ln (x + 1) - 0.098 .

Explanation:

As you can see in the problem the asymptote is x = -1. This means that the function is not defined for x= -1 and as you know, natural logarithm is not defined for zero. So, it implies that when x tends to -1 the function tends to infinite. So it must be a number adding to x that makes -1 + b = 0 ⇒ b= 1.

Then, you have y = ln (x + 1). If you check, when you replace the point given in the problem (2,1), you find that y = ln (2 + 1) ⇒ y = ln(3) ⇒ y = 1.098, so you can introduce a correction factor ⇒ y = ln (x + 1) - 0.098.

Summarizing, the function decribed before can be y = ln (x + 1) - 0.098.