Sketching polynomial and reciprocal graphsAQA A-Level Maths: Mind map

Exam questions on Sketching polynomial and reciprocal graphs

1. The curve $C$ has equation $y=(x+2)(x-1)^2$.
   Write down the coordinates of the point where $C$ touches the $x$-axis, and describe the behaviour of $y$ as $x\to-\infty$.2 marks
2. The curve $D$ has equation $y=\dfrac{4}{x^2}$.
   Write down the equations of the asymptotes of $D$, and explain why $D$ never meets the $x$-axis.2 marks
3. The curve $E$ has equation $y=x^2(3-x)$.
   Find the coordinates of the points where $E$ meets the $x$-axis and state, with a reason, whether $E$ crosses or touches the $x$-axis at each of them.3 marks