2019 H2 Mathematics Paper 2 Question 2

Graphs and Transformations

Answers

(i)

x=−83{x=- \frac{8}{3}}
x=1{x=1}
y=0{y=0}
(0,−14),(2,0){\left(0, -\frac{1}{4}\right), \left(2,0\right)}

(ii)

x<−83{x<- \frac{8}{3}} or 1<x<2{1 < x < 2}

(iii)

−83<x<1{- \frac{8}{3}<x<1} or x>2{x > 2}

Full solutions

(i)

2−x3x2+5x−8=2−x(3x+8)(x−1)\frac{2 - x}{3 x^2 + 5 x - 8} = \frac{2 - x}{(3 x + 8)(x - 1)}

(ii)

From the graph, solution of the inequality:
x<−83   or   1<x<2  ■x<- \frac{8}{3} \; \textrm{ or } \; 1 < x < 2 \; \blacksquare

(iii)

x−23x2+5x−8>02−x3x2+5x−8<0\begin{align*} \frac{x-2}{3 x^2 + 5 x - 8} &> 0 \\ \frac{2-x}{3 x^2 + 5 x - 8} &< 0 \end{align*}
From the graph, solution of the inequality:
−83<x<1   or   x>2  ■- \frac{8}{3}<x<1 \; \textrm{ or } \; x > 2 \; \blacksquare