Question

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

Answer 1

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
https://study.com/academy/lesson/vertical-asymptotes-definition-rules-quiz.html

The x-intercept in this function is 0. The coordinate is (0,0). To find the x-intercept, you put the function into your calculator and if it's on a whole number point you can easily tell where the point lies. If it is not a whole number point, you can use the settings on your graphing calculator to find the "zeroes".

The vertical asymptote is -1. To figure this out you look at the `(x+1)` 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, `(x+1)`
Since the vertical asymptote is "blocking off" the graph from being on the other side of -1, this means the domain is `x> -1`