Question

18. Given that f(x) = 3*, identify the function g(x) shown in the figure.

Answer 1

Since g(x) is a positive function (the values are positive for all x), the options A. and B. are not correct, because -3^x is a negative number bigger than +2 or -2 for some values of x.

Then, in order to check for C. and D., let's find the value of g(x) in each case for x = 0:

C.

`\begin{gathered} g\mleft(x\mright)=3^(-x)+2 \\ g(0)=3^0+2 \\ g(0)=1+2=3 \end{gathered}`

D.

`\begin{gathered} g(x)=3^(-x)-2 \\ g(0)=3^0-2 \\ g(0)=1-2=-1 \end{gathered}`

Looking at the graph, for x = 0 we have g(0) = 3, therefore the correct option is C.