Question

How to graph y=log3(x+3) and what is its Asymptote, Domain, and Range

Answer 1

The asymptote is $x=-3$

Domain is $(-3, \infty)$

Range is $(-\infty, \infty)$

Explanation:

Given that the function is $y=\log _{3}(x+3)$

Asymptote:

The function has no horizontal asymptote.

The given function is of the form, $f(x)=c \cdot \log _{a}(x+h)+k$ has a vertical asymptote $x=-h$

where $h=3$

Thus, the vertical asymptote is $x=-3$

Domain:

The domain of the function is the set of all independent x - values for which the function is real and well defined.

Let us find the positive values for log

Thus, we have,

$x+3>0$

     $x>-3$

Thus, the function domain in interval notation is $(-3, \infty)$

Range:

The range of the function is the set of all dependent y - values of the function.

Hence, the range of the function is $(-\infty, \infty)$