Question

graph g(x)=3^(x+3), and find the domain and range using the interval notation.

Answer 1

\[\mathrm{Domain\:of\:}\:3^{x+3}\::\quad \begin{bmatrix}\mathrm{Solution:}\: & \:-\infty \:<x<\infty \\\:\mathrm{Interval\:Notation:} & \:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\]

Answer 2

\[\mathrm{Range\:of\:}3^{x+3}:\quad \begin{bmatrix}\mathrm{Solution:}\: & \:f\left(x\right)>0\: \\\:\mathrm{Interval\:Notation:} & \:\left(0,\:\infty \:\right)\end{bmatrix}\]

Answer 3

are you understand @Kimes

Answer 4

I'm gonna provide more information.
for the domain... since the function given isn't a fraction and there are no restrictions, we have all real numbers or in interval notation (-oo,oo). I gotta think about it for the range.

Answer 5

ah. first we need to graph this equation
\[g(x) = 3^{x+3}\]
by letting x be any number

so if x =-1,0,1
\[g(-1) = 3^{0-1}=3^{-1}=\frac{1}{3^1} =\frac{1}{3}\]
\[g(0) = 3^{0+3}=3^3=27\]
\[g(1) = 3^{1+3}=3^4=81\]

the domain is in the x-axis and the range is in the y-axis. I already mentioned about the function not having any restrictions due to not being a fraction, so yes domain is all real numbers or in interval notation (-oo,oo). Range is in the y-axis and we have to examime the graph. We noticed that the graph starts at y =0 and continues to go up up up, so for the range we have (0,oo) or I think it's written as all real numbers greater than 0 for the range.
I'm going to attach a graph instead because graphing this manually is painful D: