what are the domain and the range of this function? (f(x)=log(x + 3)-2) \n\na. domain: ((-3,infty)); range…

what are the domain and the range of this function? (f(x)=log(x + 3)-2) \n\na. domain: ((-3,infty)); range: ((-infty,2)) \nb. domain: ((3,infty)); range: ((-infty,2)) \nc. domain: ((3,infty)); range: ((-infty,infty)) \nd. domain: ((-3,infty)); range: ((-infty,infty))

what are the domain and the range of this function? (f(x)=log(x + 3)-2) \n\na. domain: ((-3,infty)); range: ((-infty,2)) \nb. domain: ((3,infty)); range: ((-infty,2)) \nc. domain: ((3,infty)); range: ((-infty,infty)) \nd. domain: ((-3,infty)); range: ((-infty,infty))

Answer

Explanation:

Step1: Find the domain

The argument of the logarithm must be positive. So we set $x + 3>0$. Solving for $x$ gives $x>- 3$. So the domain is $(-3,\infty)$.

Step2: Find the range

The range of the basic logarithmic function $y = \log(u)$ is $(-\infty,\infty)$. For the function $y=\log(x + 3)-2$, vertical - shift does not change the range. So the range is $(-\infty,\infty)$.

Answer:

D. domain: $(-3,\infty)$; range: $(-\infty,\infty)$