Question

Analyzing a Graph In Exercise, analyze and sketch the graph of the function. Label any relative extrema, points of inflection, and asymptotes.

y = In(x + 3)

Answer 1

analyzed & sketched

Explanation:

We are given the function: y = In(x + 3)

So first we need to take the first derivative to find the interval of increase and decrease, then the second derivative to find the interval of concave up and concave down.

`y'=(1)/(x+3)`

`y''=-(1)/((x+3)^2)`

So it is always increasing function, and always concave down function.

Since it is a logarithmic function, x>3.

So, x = 3 is vertical asymptote.

I attached the sketch as a picture.