The function f is defined by f(x)= 2/(x-3) + x - 6 . Determine the coordinates of the points where the graph of f intersects the coordinate axes.

If you look at a set of x,y-axes, and imagine any curve going through both axes (you don't have to be able to imagine what this graph of f looks like just yet). Now imagine the part of the graph that crosses the x axis, this could happen at any point along the x axis, depending on the graph you're imagining, but one thing we know for certain is that when the graph crosses the x-axis, we must be along the line y=0, i.e the value on the y-axis must be zero. this is why, to find the crossing point of the graph of f with the x-axis, all we need to do is set y=0, or f(x)=0 in this case, and rearrange from there. We will get a quadratic equation, which we can easily factorise to see that 0=(x-4)(x-5), meaning that the x-axis crossing points are (4,0) and (5,0). We can also reverse this argument, the y-axis crossing point must happen when x=0, so all we have to do here is plug x=0 into the equation for f, i.e, we need to calculate f(0), simple rearranging gives us the crossing point (0,-20/3).