Question

Give an example of a decreasing logarithmic function that has a positive y-intercept.

Answer 1

Answer: f(x) = -ln(x + 1) + 3

Explanation:

We want it to be decreasing, then we can write it, for a start, as:

f(x) = -ln(x)

Ok, now we want it to have a positive y intercept, then we can add a real number inside the logarithm, and other outside: such that f(0) = positive number.

f(x) = -ln(x + 1) + 3

Now, when x = 0 we have:

f(0) = -ln(1) + 3 = 0 + 3 = 3

Then we have a decreasing logarithmic function, with an y-intercept larger than zero.