Question

Which graph represents the given exponential function?5(3)" - 1A.y14+1х-42NN+yB.421→X-4-2242-4-C.у42- 224нх2.4

Answer 1

Given the exponential function:

`f(x)=5(3)^x-1`

Let's substitute x by -1, 0, and 1 to compare with the graphs.

First, substituting x by -1:

`\begin{gathered} f(-1)=5(3)^(-1)-1 \\ f(-1)=(5)/(3)-1 \\ f(-1)=(5-3)/(3)=(2)/(3) \end{gathered}`

Second, let's substitute x by 0:

`\begin{gathered} f(0)=5(3)^0-1 \\ f(0)=5*1-1 \\ f(0)=5-1 \\ f(0)=4 \end{gathered}`

Third, let's substitute x by 1:

`\begin{gathered} f(1)=5(3)-1 \\ f(1)=15-1 \\ f(1)=14 \end{gathered}`

So, the graph is:

Answer: A