We have the function:
[tex]g(x)=3^x-2[/tex]
Question a.
The function represents an exponential growth because when
[tex]x\longrightarrow\infty,\text{ g(}\infty)\longrightarrow3^{\infty}\longrightarrow\infty[/tex]
that is, y goes to + infinity
Question b.
The y-intercept ocurrs when x=0, that is
[tex]\begin{gathered} g(0)=3^0-2 \\ g(0)=1-2 \\ g(0)=-1 \end{gathered}[/tex]
that is, the y-intercept is -1.
Question c.
The horizontal asymptote is at g(x)= -2
Question d.
The graph is:
