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

The asymptote is

Domain is

Range is

Explanation:

Given that the function is

Asymptote:

The function has no horizontal asymptote.

The given function is of the form, has a vertical asymptote

where

Thus, the vertical asymptote is

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,

Thus, the function domain in interval notation is

Range:

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

Hence, the range of the function is

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: