Solution:
The function is given below as
[tex]f(x)=\log_3(x+1)+2[/tex]
When x=0
[tex]\begin{gathered} f(x)=\operatorname{\log}_{3}(x+1)+2 \\ y=\log_3(0+1)+2 \\ y=2 \\ (0,2) \end{gathered}[/tex]
When y=0
[tex]\begin{gathered} f(x)=\operatorname{\log}_{3}(x+1)+2 \\ 0=\operatorname{\log}_3(x+1)+2 \\ \operatorname{\log}_3(x+1)=-2 \\ x+1=3^{-2} \\ x=\frac{1}{9}-1 \\ x=-0.889 \\ (-0.889,0) \end{gathered}[/tex]
When x=2
[tex]\begin{gathered} f(x)=\operatorname{\log}_3(x+1)+2 \\ y=\log_3(2+1)+2 \\ y=\log_33+2 \\ y=1+2 \\ y=3 \\ (2,3) \end{gathered}[/tex]
Using a graphing calculator, we will have the graph be
