Maths Paper 1, November 2024, question 4.3

The function $g$ is defined by $g(x)=b^x-2$ where $b>0$. The point $P(2;-\frac{7}{4})$ lies on $g$. Draw a neat sketch of $g$ on your own set of axes, labelling where it cuts each axis and giving the equation of any asymptote.