Sketching graphs of functionsEdexcel International A Level Maths: Mind map

Exam questions on Sketching graphs of functions

1. The curve $C$ has equation $y=\frac{3}{x}$, for $x\neq0$.
   Find the coordinates of the points where $C$ meets the line $y=x$.2 marks
2. The curve $D$ has equation $y=x^2(x-4)$.
   Use the shape of $D$ to explain why the equation $x^2(x-4)=5$ has exactly one real root.2 marks
3. For $0^\circ\le x\le360^\circ$, consider the curves $y=\sin x$ and $y=\cos x$.
   Explain, using the shape of the two graphs, how many solutions there are to $\sin x=\cos x$ in this interval, and find them.3 marks