What is the answer for question 8) ? http://postimg.org/image/5gm0wsol3/

Expert Answers
crmhaske eNotes educator| Certified Educator

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:


10^0=x+3=1 ->x=-2

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.