Example 5 Self Tutor
Consider f(x)=3 x¡ 9
x^2 ¡x¡ 2:
a Use your graphics calculator to obtain a sketch of the function.
b State the equations of the asymptotes of the function.
c State the axes intercepts of the function.
d Describe the turning points of the function.abhorizontal asymptote is y=0
vertical asymptotes are x=¡ 1 , x=2c x-intercept is 3 , y-intercept is (^412)
d local maximum(5,^13 ),
local minimum(1,3)
EXERCISE 23C.1
1 For these quadratic functions, find:
i the turning point ii they-intercept iii thex-intercepts
a y=x^2 ¡ 3 b f(x)=2x^2 ¡ 2 x¡ 1 c f(x)=9x^2 +6x¡ 4
2 Use your graphics calculator to sketch the graphs of these modulus functions:
a y=j 2 x¡ 1 j+2 b y=jx(x¡3)j c y=j(x¡2)(x¡4)j
d y=jxj+jx¡ 2 j e y=jxj¡jx+2j f y=
̄
̄ 9 ¡x^2
̄
̄
If the graph possesses a line of symmetry, state its equation.
3 Consider f(x)=x^3 ¡ 4 x^2 +5x¡ 3 for ¡ 16 x 64 :
a Sketch the graph with help from your graphics calculator.
b Find thex- andy-intercepts of the graph.
c Find and classify any turning points of the function.
d State the range of the function.
e Create a table of values for f(x) on ¡ 16 x 64 withx-steps of 0 : 5.
4 Consider f(x)=x^4 ¡ 3 x^3 ¡ 10 x^2 ¡ 7 x+3for ¡ 46 x 66 :
a Set your calculator window to showyfrom ¡ 150 to 350. Hence sketch the graph of f(x).
b Find the largest zero of f(x).
c Find the turning point of the function near x=4.
d Adjust the window to ¡ 26 x 61 , ¡ 26 y 67. Hence sketch the function for ¡ 26 x 61.
e Find the other two turning points and classify them.
f Make a table of values for f(x) on 06 x 61 withx-steps of 0 : 1.
y
O x
local min
local max
x¡=-1 x¡=¡2
476 Further functions (Chapter 23)
IGCSE01
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Y:\HAESE\IGCSE01\IG01_23\476IGCSE01_23.CDR Monday, 27 October 2008 2:18:45 PM PETER