- The sketch below shows the graphs of ƒ(x) = log5x and g(x) = 2x - 1 + 1 T and U are the x-intercepts of g and ƒ respectively The line y=x intersects the asymptotes of g at R, and the graph of g at V.
- The graphs of the functions f(x) = a(x + p)2 + q and g(x) = kx + r + d are sketched below. Both graphs cut the y-axis at -4 One of the points of intersection of the graphs in P(1; -8), which is also the turning point of ƒ. The horizontal asymptote of g is y = -2.
- Sketched below is the parabola f, with equation f(x) = -x2 + 4x -3 and a hyperbola g. with the equation (x-p)(y + t) = 3. B, the turning point of f, lies at the point of intersection of the asymptotes of g. A(-1;0) is the x-intercept of g.