chapter 19 i graphs of functions ii enrich

8/3/2019 Chapter 19 I Graphs of Functions II ENRICH

http://slidepdf.com/reader/full/chapter-19-i-graphs-of-functions-ii-enrich 1/13

Enrichment

CHAPTER 19. GRAPHS OF FUNCTIONS II

Important Notes:

For Paper 1 (Objective Questions), the questions asked are usually related to the shapes andpositions of basic graphs of LINEAR, QUADRATIC, CUBIC and RECIPROCALFUNCTIONS.

Students are expected to be able to identify a) the shape of graph given a type of functionb) the type of function given a graphc) the graph given a function and vice versa.

The different types of functions for Paper 1, SPM Mathematics:

Linear y = mx + c

m = gradientc = y-intercept

Quadraticy = ax 2 + bx + c

Note : Paper 1 limits toy = ax 2 + c

Cubicy = ax 3 +bx 2 +cx + d

Note : Paper 1 limits to y = ax 3 + c

Reciprocal

y =a x

Note : This module concentrates on graph sketching, the skills needed for Paper 1. For details on how to plot graphs please refer to the other related modules (eg. Chapter 12 – The Straight Line – on how todraw / plot straight lines)

19.0 Back to Basic

I. Linear Graphs : can be represented by the equation y = mx + c.• m is the gradient• c the y-intercept, ie, the place where the straight line cuts the y-axis.

II. The general form of a Quadratic Function is f(x) = ax 2 + bx + c ; a, b, c are constants and a ≠ 0 .Characteristics of a quadratic function:

• Involves one variable only,• The highest power of the variable is 2.

III. The general form of a Cubic Function is f(x) = ax 3 + bx 2 + cx + d ; a, b, c and d are constants anda ≠ 0.

Characteristics of a cubic function:• Involves one variable only,• The highest power of the variable is 3.

IV. The simple Reciprocal Function is of the form y = a x

, where a is a constant.

Graphs of Functions II 1

a x

O x

y

x

x

y

O

y

O x

y

O x



Enrichment

Questions Based On Examination Format

1. Which of the following graphs represents y = x 2 – 2 ?

A. B.

C. D.

2. Which of the following equations represents the graph of a quadratic function?

A. y = 2 + x 2 B. xy = 2 C. x – y = 2 D. y = 2x –2

3. The diagram below shows a sketch of a function.

What is the equation of the function?A. y = x2 – 5B. y = – x2 – 5C. y = x3 – 5D. y = – x3 – 5


y

O

y

xO

y

xO

x

– 2 – 2

– 2

y

O– 2 x

y

xO

– 5



Enrichment

4. Which of the following graphs represents4

y x

= − ?

A. B.

C. D.

5. Which of the following graphs represents ?5 3 x y −=

A B

C D


x

y

O

y

xO

y

xO

x

y

O

y

xO

5

y

xO 5

y

xO

5

y

xO-5



Enrichment

6

Diagram 1

Diagram 1 shows the graph of 16+−= n x y . State the value of n and k .

A. n = – 1, k =16 B. n = 3, k =17 C. n = – 3, k =16 D. n = 3, k =15

7

Diagram 2

Diagram 2 shows the graph of y = x 3 + k. Find the value of h.

A. 2 B. 3 C. – 2 D. – 3

8. Which of the following equations represents a linear graph ?

A. y = 1 + x 2 B. xy = 4 C. x – y = 2 D. y = 3x –1

9. Which of the following equations represents the graph of a reciprocal function?

A. y = 1 + 2x B. y – x = 4 C. x y + 2 = 0 D. y = 3x 3

10. Which of the following represents the graph of y = x 3 – 1 ?

A B C D


( – 1, k )

x

y

0

.

O x

y

x

x

y

O

y

O

x

y

O

x

( h, 0)x

y

0.

8



Enrichment

11. Which of the following represents the graph of 10

y x

= − ?

A B C D

12.

The graph labelled G most likely represents

A. y = –2x 2 B. y = 2x 2 – 2 C. x y + 2 = 0 D. y = 2x 3

13.


A. y = x – 2 B. y = – x – 2 C. y = – x + 2 D. y = - 2x


O x

y

x x

y

O x

y

O

y

O

x

O

y

x

y = 2x 2

G

O

y

x

y = x + 2

G



Enrichment

14.


A. y =2

1x B. y = – x C. y = x + 2 D. y = 2x

15. Which of the following represents the graph of 31 y x= − ?

A B C D

16. Which of the following represents the graph of 22 y x= − ?

A B C D

17.

Diagram 3

Diagram 3 shows the graph of y = - 4xn

. Find the value of n

A. 2 B. 3 C. – 1 D. – 2


O

y

x

y = x

G

y

O

x

y

O

x

x

y

O

y

O

x

xO

y

O x

y

O x

y

O x

y

x

y

O



Enrichment

18.

The above graph represents

A. y = - x + 2 C. y = 2 – x2

B. x

y6

= D. x

y6

−=

19.

The above graph represents

A. y = – x 2 + 16 C. y = (x + 4) 2

B. y = x2 + 16 D. y = 16 – (x+4) 2

20. Which of the following does NOT represent a linear graph ?

A. y = x B. x = 2y C. xy = 2 D. y = – 2


x

y

O

x

y

O

16

4-4



Enrichment

Past-Year Questions on Graphs of Functions II

Nov 2003, Q121. Which of the following graphs represents y = x 2 – 3 ?

A. B.

C D.

Nov 2004, Q29

2. Which of the following graphs represents 2 y x

= ?

A. B.

C. D.


x

y

O

y

xO

y

xO

y

xO



Enrichment

July 2005, Q283. Diagram 12 shows a sketch of a function.

What is the equation of the function?

A. y = x2

– 3B. y = – x2 – 3C. y = x3 – 3D. y = – x3 – 3

Nov 2005, Q284. Which of the following graphs represents y = x 2 – 4 ?

A. B.

C. D.


y

xO

– 3

y

O

y

xO

y

xO

x

– 4 – 4

– 4

y

O– 4 x



Enrichment

July 2006, Q27

5. Which of the following graphs represents y =4

1−

A. B.

C. D.

Nov 2006, Q28

6. Which of the following graphs represents y = 10 – 2x 3?

A. B.

C. D.




Enrichment

Jun 2007, Q 30

7. Which of the following graphs represents y = – 5x 3 ?

A. B

C D

Nov 2007, Q 28

9 Which of the following graphs represents 52+−= x y ?

A B

C D


x

y

0 x

y

0

x

y

0

x

y

0

– 5 – 5

y

x0 5

y

x0

5

y

x0 5

y

x0

5



Enrichment

Jun 2008, Q 29

10 Which graph represents ?32

1−= x y

A B

C D

Nov 2008, Q 2711 Which graph represents 22

+−−= x x y ?

A B

C D


y

x0 –3

–6

y

x0

–3

–6

y

x0 –3

6

y

x0

–3

6

y

x0 –2 1

y

x0 2 –1

y

x0 –2 1

y

x0 –1 2



Enrichment

ANSWERS

Questions Base On Examination Format

1. A 2. A 3. B 4. D 5. C 6. D 7. C 8. C 9. C 10. D

11. C 12. B 13. C 14. A 15. B 16. D 17. C 18. B 19. A 20. C

Past-Year Questions


1 B2 D3 D4 A5 C6 B7 B8 B9 B

10 C

chapter 19 i graphs of functions ii enrich

Documents