Chapter 11 II Graphs of Functions Enrichment

7/27/2019 Chapter 11 II Graphs of Functions Enrichment

1/12

Mathematics Form 5

CHAPTER 2 : GRAPHS OF FUNCTIONS II

Steps involved in solving an equation graphically:

1. Find they value by substitutingx valueinto the given function.

2. Draw the graph by using the given scale forx-axis andy- axis.

3. Find the value ofy orx when given value ofx ory from the graph.

4. On the same axes, draw a suitable straight line which satisfies the equation.

5. Determine the solutions by reading off thex-coordinates of the point of

intersection of the two graphs.

2. 2 Quadratic Graph

Exercise 1 :

a) Complete the following table for the equation 5922

+= xxy

b) By using a scale of 2 cm to 1 unit on the x-axis and 2cm to 5 unit on the y-axis, draw the

graph of 5922

+= xxy for 70 x

c) From your graph, find

i) the value ofy, whenx = 1.7

ii) the value ofx, wheny = 15d) Draw a suitable straight line on your graph to find the values ofx which satisfy the

equation 041022

=+ xx for 70 x . State the values ofx.

Exercise 2 :


= xxy


graph of 7522

= xxy for 53 xc) From your graph, find

i) the value of y, when x = -2.5

ii) the value of x, when y = 15

d) Draw a suitable straight line on your graph to find the values of x which satisfy the

equation 04722

=+ xx for 53 x . State the values of x.

Chapter 2: Graphs of Functions 1 Prepared by: Gan K. S.

x 0 1 2 3 4 5 6 7

y 5 -2 -5 1 10 40

x -3 -2 -1 0 1 2 3 4 5

y 26 0 -7 -10 -9 5 18


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Mathematics Form 5

d) Draw a suitable straight line on your graph to find the values ofx which satisfy the

equation 011322

= xx for 53 x . State the values ofx.

2.3 : Cubic Graph

Exercise 1:


+= xxy


graph of 7123

+= xxy for 44 x


i) the value ofy, whenx = 2.5

ii) the values of negativex that satisfy the equation 7123

= xx

d) Draw a suitable straight line on your graph to find the values ofx which satisfy the

equation 02153 =+ xx for 44 x . State the values ofx.

Exercise 2:

July 2004, Q12

(a) Table 2 shows values ofx andy which satisfy the equation 1053

+= xxy .

x -3.4 -3 -2 -1 0 1 2 3 3.4

y 12.3 k 12 14 10 6 m 22 32.3

TABLE 2

Calculate the value ofkand ofm. [2 marks]

(b) For this part of the question, use the graph paper on page 33.

You may use a flexible curve rule.By using a scale of 2 cm to 1 unit on thex-axis and 2 cm to 5 units on they-axis,

draw the graph of 1053

+= xxy for -3.4 x 3.4.

[4 marks]

(c) From your graph, find

(i) the value of y whenx = 0.7 ,

(ii) the value ofx when 01053 =+ xx .[2 marks]

(d) Draw a suitable straight line on your graph to find all the values ofx which

satisfy the equation 0263

= xx for -3.4 x 3.4.

State these values ofx.

[4 marks]


x -4 -3 -2 -1 0 1 2 3 4

y -9 16 18 7 -4 -9 23


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Mathematics Form 5

Exercise 3:

(a) Complete Table 4 for the equationy= x3+ 4x+ 2, where3 x 3.

Table 4

[2 marks]

(b)By using a scale of 2 cm to 1 unit on thex-axis and 2 cm to 5 units on they-axis, draw the

graph ofy= x3+ 4x+ 2 for3 x 3. [4 marks]

(c)From your graph, find(i) the value ofy when x = 2.5,

(ii) the value ofx wheny = 13. [2 marks]

(d)Draw a suitable straight line on your graph to find the value ofx which satisfy the

equationx3+ 6x1 = 0 for3 x 3. [4 marks]

Exercise 4:a) Complete the following table for the equation 58

3+= xxy


graph of 583

+= xxy for 43 x


i) the value of y, when x = -1.4

ii) the value of x, when y= 25d) Draw a suitable straight line on your graph to find the values of x which satisfy the

equation 01123

= xx for 43 x . State the values of x.

Exercise 5:SPMNovember 2007 Q 12

(a) Complete Table 1 in the answer space for the equation3

6 xy = by writing down the

values ofy.

x 3 2.5 2 1 0 1 2 2.5

y

(b) For this part of the question, use the graph paper. You may use a flexible curve rule.

By using a scale of 2 cm to 1 unit on thex-axis and 2 cm to 5 units on the y-axis, draw

the graph of3

6 xy = for 5.23 x .


(i) the value ofy when x = 1.5 ,

(ii) the value ofx when y = 10 .

(d) Draw a suitable straight line on your graph to find the values ofx which satisfiy the

equation3

6 xy = for 5.23 x .State these values of x .


x -3 -2 -1 0 1 2 3 3.5 4

y 2 12 5 -3 19.9 37

[2 marks]

[4 marks]

[2 marks]

[4 marks]


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Mathematics Form 5


graph ofx

y6

= for 44 x

c) From your graph,

i) find the value of y, when x = 1.3

ii) find the value of x, when y = 3.5


equation xx

=+13

for 44 x . State the values of x.

Exercise 3:

a) Complete the following table for the equationx

y 2=


graph ofx

y2

= for 44 x

c) From your graph,i) find the value of y, when x = 1.5

ii) find the value of x, when y = -1.8


equationx

x4

12 =+ for 44 x . State the values of x.

Exercise 4:


x -4 -2.5 -1 -0.6 0.6 1 2 3 4

y 1.5 6 10 -10 -6 -3 -1.5

x -4 -3 -2 -1 -0.5 0.5 1 2 3 4

y -0.5 -0.7 -1 -2 4 1 0.7 0.5


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Mathematics Form 5

a) Complete the following table for the equationx

y4

=

b) By using a scale of 2 cm to 1 unit on the x-axis and 2cm to 2unit on the y-axis, draw the

graph ofx

y4

= for 55 x

c) From your graph,

i) find the value of y, when x = -1.4

ii) find the value of x, when y = 4.4


equation 02

3= x

xfor 45.0 x . State the values of x.

Exercise 5:

a) Complete the following table for the equation 123 +=x

y

b) By using a scale of 2 cm to 0.5 unit on the x-axis and 2cm to 0.5unit on the y-axis, draw

the graph of 12

3+=

xy for 45.0 x

c) From your graph,

i) find the value of y, when x = 1.3ii) find the value of x, when y = 2.8


equation 02

3= x

xfor 45.0 x . State the values of x.


x -5 -4 -2 -1 -0.5 0.5 0.8 1.5 2.5 5

y -1 -4 -8 8 5 1.6

x 0.5 1 1.5 2 2.5 3 3.5 4

y 4 2.5 1.75 1.6 1.43 1.38


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Mathematics Form 5

PAST YEAR EXAMINATION QUESTIONS

1. Nov 2003, Q12

(b) Complete the following table for the equationx

y4

= .

(c)

x -4 -2.5 -1 -0.5 0.5 1 2 3.2 4

y 1 1.6 8 -8 -4 -1.25 -1

[2 marks]

(d) For this part of the question, use the graph paper. You may use a flexible curve.

By using a scale of 2 cm to 1 unit on thex-axis and 2 cm to 2 units on they-axis,

draw the graph ofx

y4

= for -4 x 4.

[5 marks](e) From your graph, find

(i) the value of y whenx = 1.8,

(ii) the value of x wheny = 3.4.

[2 marks]

(f) Draw a suitable straight line on your graph to find all the values ofx which


+= xx

for -4 x 4.


[3 marks]

2. July 2004, Q12

(b) Table 2 shows values ofx andy which satisfy the equation 1053 += xxy .

x -3.4 -3 -2 -1 0 1 2 3 3.4

y 12.3 k 12 14 10 6 m 22 32.3

TABLE 2


(d) For this part of the question, use the graph paper on page 33.

You may use a flexible curve rule.By using a scale of 2 cm to 1 unit on thex-axis and 2 cm to 5 units on they-axis,


+= xxy for -3.4 x 3.4.

[4 marks]

(e) From your graph, find

(i) the value of y whenx = 0.7 ,

(ii) the value ofx when 01053 =+ xx .[2 marks]



9/12

Mathematics Form 5



= xx for -3.4 x 3.4.


[4 marks]

Answer:

(a) k = ..

m = .

(b) Refer graph on page 33

(c) (i) y = ..

(ii) x = .

(d) x = ..

3. Nov 2004, Q12

(a) Table 1 shows values of x andy which satisfy the equation 3422

= xxy .

x -2 -1 0 1 2 3 4 4.5 5

y k 3 -3 -5 -3 m 13 19.5 27

Table 1


(b) For this part of the question, use the graph paper. You may use a flexible curve.



= xxy for -2 x 5.

[5 marks]


i. the value ofy whenx = -1.5,ii. the value ofx wheny = 0.

[2 marks](d) Draw a suitable straight line on your graph to find a value ofx which satisfies the

equation 02322

=+ xx for -2 x 5.

State this value ofx.

[3 marks]

4. Nov 2005, Q12



10/12

Mathematics Form 5

(a) Complete Table 2 for equation 32 2 = xxy .

x -2 -1 0.5 1 2 3 4 4.5 5

y 7 -2 -2 3 12 33 42

Table 2

[2 marks]

(b) For this part of the question, use the graph paper. You may use a flexible curve.

By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-

axis, draw the graph of 322

= xxy for -2 x 5.

[4 marks]

(c) From your graph, findi. the value ofy whenx = 3.6,

ii. the value ofx wheny = 37.

[2 marks]

(d) Draw a suitable straight line on your graph to find all value ofx which satisfy the

equation 1032

2

= xx for -2 x 5.State these values ofx.

5. July 2005, Q12

(a) Complete Table 1 in the answer space for the equation2

23 xxy = .

[2 mark]

Answer:

(a)

x -3 -2 -1 0 1 2 3 3.5 4y -12 -3 3 0 -7 -25 -33

TABLE 1

(b) For this part of the question, use the graph paper provided on page 33.

You may use a flexible curve rule.


draw the graph of 223 xxy = for -3 x 4.

[4 marks]

Answer:

(c) Refer graph on page 33 .


(i) the value ofy when x = 1.7 ,




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Mathematics Form 5

Answer:

(c) (i) y = .

(ii) x =



118

2=+ xx for -3 x 4.


[4 marks]

Answer:

(d) x = ,

6. July 2006, Q12

(a) Complete Table 2 in the answer space for the equation 383 += xxy

by writing down the values ofy when x = -2 and 2 .

[2 marks ]

(b) For this part of the question, use the graph paper provided on page 35.

You may use a flexible curve rule.



+= xxy for -3.5 x 3.5 .

[4 marks]

(c) From your graph, find(i) the value ofy when x = 0.7 ,


[2 marks ]



= xx for -3.5 x 3.5 .


[4 marks]

Answer:

(a)

x -3 -2 -1 0 1 2 3 3.5 4y -12 -3 3 0 -7 -25 -33

TABLE 1

(b) Refer graph on page 33 .

(c) (i) y = .



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Mathematics Form 5

(ii) x =

(d) x = ,

7. Nov 2006, Q13

(a) Complete Table 1 in the answer space for the equation y =x

24by writing down

the value of y when x = -3 and x = 1.5. [2 marks ]

(b) For this part of the question, use the graph paper provided on page 35. You may

use a flexible curve rule.

By using a scale of 2cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis,

draw the graph of y =

x

24for 44 x . [5 marks ]


i. the value of y when x = 2.9ii. the value of x when y = -13.

[ 2 marks ]

(d) Draw a suitable line on your graph to find a value of x which satisfies theequation 2x2 + 5x = 24 for 44 x .

State this value of x.[ 3 marks ]

Answer :

(a)

x -4 -3 -2 -1 1 1.5 2 3 4

y -6 -12 -24 24 12 8 6

TABLE 1

(b) Refer graph on page 35

(c) (i) y = ..

(ii) x = ..

(d) x = ..


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Chapter 11 II Graphs of Functions Enrichment