Question 1

Graph the functionf(x) = log3(x+1) + 2

Question 2

Solution:

The function is given below as

$f(x)=\log_3(x+1)+2$

When x=0

$\begin{gathered} f(x)=\operatorname{\log}_(3)(x+1)+2 \\ y=\log_3(0+1)+2 \\ y=2 \\ (0,2) \end{gathered}$

When y=0

$\begin{gathered} f(x)=\operatorname{\log}_(3)(x+1)+2 \\ 0=\operatorname{\log}_3(x+1)+2 \\ \operatorname{\log}_3(x+1)=-2 \\ x+1=3^(-2) \\ x=(1)/(9)-1 \\ x=-0.889 \\ (-0.889,0) \end{gathered}$

When x=2

$\begin{gathered} f(x)=\operatorname{\log}_3(x+1)+2 \\ y=\log_3(2+1)+2 \\ y=\log_33+2 \\ y=1+2 \\ y=3 \\ (2,3) \end{gathered}$

Using a graphing calculator, we will have the graph be

Graph the functionf(x) = log3(x+1) + 2-example-1

Graph the functionf(x) = log3(x+1) + 2-example-2

Graph the functionf(x) = log3(x+1) + 2-example-3

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