The y-intercept is the point where the graph cuts the y-axis. The y-axis is the line x = 0, therefore, to find the y-coordinate of this point we just need to evaluate x = 0 in our function.
[tex]\begin{gathered} y(x)=b^x-2 \\ y(0)=b^0-2 \end{gathered}[/tex]
Any nonzero real number raised to the power of zero is one, therefore
[tex]y(0)=b^0-2=1-2=-1[/tex]
The y-intercept is (0, -1).
