Question

For the curve y = log(x+3)

determine the following:

a) asymptotes, if any.

b) intercepts, if any.

c) domain and range

Answer 1

you should be familiar with the function
y = log x , which has the y-axis as an asymptote
this one is simply moved to the left 3 units

so the vertical asymptote is x = -3
intercepts :
for y-intercepts let x = 0 --- y = log3
for x-intercepts let y = 0
then log(x+3) = 0
we know log 1 = 0, so x+3 = 1
x = -2

domain: from our definition of logs, x+3 > 0 ---> x > -3
from knowing the basic graph, the range is any real number.