An asymptote is a line for which the function approaches infinity or becomes undefined as the distance between the function and the line approaches 0.
For the function y=log(x+3), y is undefined at x=-3 because the log of any number less than or equal to zero does not exist.
Therefore there is a vertical asymptote at x=-3
In order to determine if there is a horizontal asymptote, we must rearrange the equation to be a function for x:
There is no horizontal asymptote because as y approaches infinity so does x.
The x-intercept exists when y=0:
Therefore the x-intercept is at (-2,0)
The y-intercept exists when x=0:
Therefore the y-intercept is at (0,0.48)
The domain of a function is the range of all possible x values. The domain of y=log(x+3) is x>-3
The range of a function is the range of all possibly y values. The range of y=log(x+3) is `-ooltyltoo` because the integer 10 can be raised to all real exponents.