# How do you find the domain, x intercept and vertical asymptotes of f(x)=log_10(x+1)?

Feb 25, 2018

here is what the graph looks like:

#### Explanation:

To start off I will explain what the domain, x-intercept, and vertical asymptotes are.

domain: the set of values of the independent variable(s) for which a function or relation is defined
http://www.mathwords.com/d/domain.htm

x-intercept: the x-coordinate of a point where a line, curve, or surface intersects the x-axis
https://www.merriam-webster.com/dictionary/x-intercept

vertical asymptote: invisible vertical lines that certain functions approach, yet do not cross, when the function is graphed
The vertical asymptote is -1. To figure this out you look at the $\left(x + 1\right)$ in the function, you can see that there is a 1 in the brackets. Therefore, the vertical asymptote becomes $x = - 1$
The domain is similar to the vertical asymptote because you look at the same part of the function, $\left(x + 1\right)$
Since the vertical asymptote is "blocking off" the graph from being on the other side of -1, this means the domain is $x > - 1$