Y11 MATHEMATICS ADVANCED
LESSON 5: REAL FUNCTIONS 4
Notice to Students

Attempt ALL questions.

INCOMPLETE Work Booklets will NOT be marked. If you are having difficulty with
your Work Booklet, please seek assistance through ADDITIONAL SUPPORT
(WORKSHOP) on Sundays.

The grading for your Work Booklet will be recorded for reporting purposes.

Allocated time for this Work Booklet is 60 minutes.
Copyright © MATRIX EDUCATION 2014
Page 57 of 124
OUR STUDENTS COME FIRST.
All rights reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any
form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior permission of Matrix Education.
Y11 MATHEMATICS ADVANCED
LESSON 5: REAL FUNCTIONS 4
GRAPHS WITH ABSOLUTE VALUES
Question 1
Sketch the following graphs and state the domain and range of each.
(i)
y  2x  5
(ii)
y  3 x
[1]
[2]
Copyright © MATRIX EDUCATION 2014
Page 58 of 124
OUR STUDENTS COME FIRST.
All rights reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any
form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior permission of Matrix Education.
Y11 MATHEMATICS ADVANCED
LESSON 5: REAL FUNCTIONS 4
Question 2
(i)
On the same coordinate plane draw the graphs of y  2 x  3 and y  x  1
(ii)
Hence solve 2 x  3  x  1
[3]
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
Copyright © MATRIX EDUCATION 2014
Page 59 of 124
OUR STUDENTS COME FIRST.
All rights reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any
form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior permission of Matrix Education.
Y11 MATHEMATICS ADVANCED
LESSON 5: REAL FUNCTIONS 4
PIECE-MEAL GRAPHS
Question 1
 x; x  0

A function is defined as f  x   2 x; 0  x  2
x 2 ; x  2

Evaluate the following:
(i)
f  2
[4]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(ii)
f
 5
[5]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(iii)
 1 
f

1 2 
[6]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
(iv)

f 2 k2

[7]
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
Copyright © MATRIX EDUCATION 2014
Page 60 of 124
OUR STUDENTS COME FIRST.
All rights reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any
form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior permission of Matrix Education.
Y11 MATHEMATICS ADVANCED
LESSON 5: REAL FUNCTIONS 4
Question 2
3 x  2; x  0

Given h x   ax  b; 0  x  3
5  2 x; x  3

(i)
Given that
h 1  h1 and h2  h4 , find the values of a and b.
[8]
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
(ii)
Sketch the curve
y  hx and state its range.
Copyright © MATRIX EDUCATION 2014
[9]
Page 61 of 124
OUR STUDENTS COME FIRST.
All rights reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any
form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior permission of Matrix Education.
Y11 MATHEMATICS ADVANCED
LESSON 5: REAL FUNCTIONS 4
Question 3
 x 2  4; x  2

Consider f x    3x  1;  2  x  2
1  2  x x  2

(i)
Evaluate
f  1  f  3  2 f 3
[10]
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
y  f x 
(ii)
Sketch
(iii)
State the range of
f x 
[11]
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
Copyright © MATRIX EDUCATION 2014
Page 62 of 124
OUR STUDENTS COME FIRST.
All rights reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any
form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior permission of Matrix Education.
Y11 MATHEMATICS ADVANCED
LESSON 5: REAL FUNCTIONS 4
REGIONS
Question 1
Sketch the following regions on separate diagrams
(i)
1  x  y  2
(ii)
1  x2  y2  9
Copyright © MATRIX EDUCATION 2014
Page 63 of 124
OUR STUDENTS COME FIRST.
All rights reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any
form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior permission of Matrix Education.
Y11 MATHEMATICS ADVANCED
(iii)
y  2x 1
(iv)
y
LESSON 5: REAL FUNCTIONS 4
4
2 x
Copyright © MATRIX EDUCATION 2014
Page 64 of 124
OUR STUDENTS COME FIRST.
All rights reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any
form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior permission of Matrix Education.
Y11 MATHEMATICS ADVANCED
(v)
y
(vi)
y  25  x 2
LESSON 5: REAL FUNCTIONS 4
4 x
Copyright © MATRIX EDUCATION 2014
Page 65 of 124
OUR STUDENTS COME FIRST.
All rights reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any
form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior permission of Matrix Education.
Y11 MATHEMATICS ADVANCED
LESSON 5: REAL FUNCTIONS 4
Question 2
Sketch the regions where the following inequalities hold simultaneously.
(i)
y  9  x 2 and y  2 x  1
(ii)
y  25  x 2 and y  2 x  5
Copyright © MATRIX EDUCATION 2014
Page 66 of 124
OUR STUDENTS COME FIRST.
All rights reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any
form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior permission of Matrix Education.
Y11 MATHEMATICS ADVANCED
LESSON 5: REAL FUNCTIONS 4
Question 3
The diagram shows a ABC on a number plane.
y
A
x
0
B
C
Write three inequalities that would best describe the region inside ABC .
[12]
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
……………………………………………………………………………………………………………
Copyright © MATRIX EDUCATION 2014
Page 67 of 124
OUR STUDENTS COME FIRST.
All rights reserved. No part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any
form, or by any means (electronic, mechanical, photocopying, recording, or otherwise), without the prior permission of Matrix Education.