Sketching graphs of functionsEdexcel International A Level Maths: Flashcards

What these 13 flashcards ask

What does a cubic with a positive x^3 coefficient do as x\to\pm\infty?
What does a repeated root mean for a graph?
Which quadrants contain y=\frac kx for k0?
Which quadrants contain y=\frac k{x^2} for k0?
Asymptotes of y=\frac kx?
What is an asymptote?
Period of \sin x and \cos x?
Period of \tan x?
Where are the asymptotes of \tan x for 0^\circ\le x\le360^\circ?
Maximum and minimum values of y=\sin x?
How do graphs show the solutions of f(x)=g(x)?
Solve \sin x=\cos x for 0^\circ\le x\le360^\circ.
Sketch features of y=x(x-2)(x+2).

Exam questions on Sketching graphs of functions

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).