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

Answer:

analyzed & sketched

Step-by-step 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.

$y'=\frac{1}{x+3}$

$y''=-\frac{1}{(x+3)^2}$

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.