Given:
[tex]y=\mleft(\frac{5}{2}\mright)^x[/tex]
To sketch the graph:
First find the three points.
Put x=-1 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^{-1} \\ =\frac{2}{5} \\ =0.4 \end{gathered}[/tex]
Put x=0 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^0 \\ =1 \end{gathered}[/tex]
Put x=1 we get,
[tex]\begin{gathered} y=(\frac{5}{2})^1 \\ =2.5 \end{gathered}[/tex]
Therefore, the three points are, (-1, 0.4), (0, 1), and (1, 2.5).
The graph is,
