Given the exponential function:
[tex]f(x)=5(3)^x-1[/tex]
Let's substitute x by -1, 0, and 1 to compare with the graphs.
First, substituting x by -1:
[tex]\begin{gathered} f(-1)=5(3)^{-1}-1 \\ f(-1)=\frac{5}{3}-1 \\ f(-1)=\frac{5-3}{3}=\frac{2}{3} \end{gathered}[/tex]
Second, let's substitute x by 0:
[tex]\begin{gathered} f(0)=5(3)^0-1 \\ f(0)=5*1-1 \\ f(0)=5-1 \\ f(0)=4 \end{gathered}[/tex]
Third, let's substitute x by 1:
[tex]\begin{gathered} f(1)=5(3)-1 \\ f(1)=15-1 \\ f(1)=14 \end{gathered}[/tex]
So, the graph is:
Answer: A
