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

1 Answer
Feb 25, 2018

here is what the graph looks like:
enter image source here


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

x-intercept: the x-coordinate of a point where a line, curve, or surface intersects the x-axis

vertical asymptote: invisible vertical lines that certain functions approach, yet do not cross, when the function is graphed

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#