MODULE 10-Graphs of Functions

7/17/2019 MODULE 10-Graphs of Functions

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MODUL 10SKIM TIUSYEN FELDA (STF) MATEMATIK SPM “ENRICHMENT”

TOPIC : GRAPHS OF FUNCTIONSTIME : 2 HOURS

1. a) Complete Table 1 in the answer space for the equation y = 2x2 – 5x – 3.

1b) or this part! use a "raph paper.

#y usin" a scale 2 cm to 1 unit on the x$axis an% 2 cm to 5 units on the y$axis! %raw the "raph of y = 2x2 – 5x – 3 for $3 & x & 5.

1c) rom your "raph! fin%

1. i) the 'alue of y when x = $2.(!ii) the 'alue of x when 2x2 – 5x – 3 = .

1%) *raw a suitable strai"ht line on your "raph to fin% all the 'alues of x which satisfy theequation 2x2 – +x = , for $3 & x & 5.

-tate these 'alues of x.

nswer/

a)

0 $3 $2 $1 .

3 ( $3

Table 1

c) i) y =

ii) x =



%) x =

2. a) Complete Table 2 in the answer space for the equation y = x 2 – 5x (.


#y usin" a scale 2 cm to 1 unit on the x$axis an% 2 cm to 5 units on the y$axis! %raw the "raph of y = x2 – 5x ( for & x & +.


1. a. the 'alue of y when x = (.5!b. the 'alue of x when y = 21.,5

1%) *raw a suitable strai"ht line on your "raph to fin% all the 'alues of x which

satisfy the equation x2 – ,x 3 = for & x & +.-tate these 'alues of x.

nswer/

a)

0 1 2 2.5 3

( $2 $

Table 2

c) i) y =



ii) x =

%) x =

3. a) Complete Table 3 in the answer space for the equation y = .


#y usin" a scale 2 cm to 1 unit on the x$axis an% 2 cm to 2 units on the

y$axis! %raw the "raph of y = for $5 & x & 5.


1. a. the 'alue of y when x = 1.+!b. the 'alue of x when y = $.

1%) rom your "raph! fin% all the 'alues of x with the con%ition that the 'alue

of y is three times the 'alue of x.

nswer/



a)

0 $5 $3 $2 $1 $.5

$1 $1., $2.5 $1

Table 3

c) i) y =

ii) x =

%) x =

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


#y usin" a scale 2 cm to 1 unit on the x$axis an% 2 cm to 1 units on the y$axis! %raw the

"raph of y = for $( & x & (.


1. a. the 'alue of y when x = $1.5!



b. the 'alue of x when y = 1.2.


satisfy the equation = x $ 2 for $( & x & (.-tate these 'alues of x.

nswer/

a)

0 $( $2.5 $2 $1 $.5 $.5 $.+ $2 $(

Table (

c) i) y =

ii) x =

%) x =

5. a) Complete Table 5 in the answer space for the equationy = x3 – 13x 1+.




#y usin" a scale 2 cm to 1 unit on the x$axis an% 2 cm to 5 units on the y$axis! %raw the "raph of y = x3 – 13x 1+ for $( & x & (.


1. a. the 'alue of y when x = $1.5!b. the 'alue of x when y = 25.


satisfy the equation x3 – 11x – 2 = for $( & x & (.-tate these 'alues of x.

nswer/

a)

0 $( $3 $2 $1

3 3 1+

Table 5

c) i) y =

ii) x =

%) x =



. a) Complete Table in the answer space for the equationy = x3 x2 – 12x – 5.


#y usin" a scale 2 cm to 1 unit on the x$axis an% 2 cm to 5 units on the y$axis! %raw the "raph of y = x3 x2 – 12x – 5 for $( & x & (.


1. a. the 'alue of y when x = .5!b. the 'alue of x when 11.4.


satisfy the equation x3 x2 – 1x = for $( & x & (.-tate these 'alues of x.

nswer/

a)

0 $( $3 $2 $1

$5 13 , $5

Table

c) i) y =

ii) x =



%) x =

MODULE 10 – ANSWERSTOPIC: GRAPHS OF FUNCTIONS

1. a) x=$2 y=15 x=.5 y= $5 x=3 y=

b) "raph

c) i) x=$2.( y= 2.5ii) when 2x2 – 5x – 3 =

y =



Then the 'alues of x is $.5 an% 3

1e) y=2x2$5x$3

=2x2$+x$, $)$$$$$$$$$$$$$$$$$$$$$$$

= 3x (

0 3 ( 13

rom the "raph x= $.,5 an% (.,5

2. a)x=2.5 y=$2.25 x=( y=

b)"raph 2

c) i) y=1.,5ii) x=,.(

1e)



strai"ht line y=2x1x=.(5 an% .55

3. a) x=$1 y=$5 x=2.5 y=2

b)"raph

c) i) x=1.+ y= 2.+ii) y=$ x=$.+

1e) The "raph is y=3x

0 2

The 'alues of x= $1.3 an% 1.3



(. a) x=$2 y=$1 x=2.5 y=.+

b) "raph

c) i) y=$1.3ii) x=1.,

e) The strai"ht line is y= x – 2

The 'alues of x = $.,5 an% 3.(5

5. a) x=$3 y=3 x=2 y=b) "raph



c) i) x=$1.5 y=3(ii) y=25 x=3.+5

1e) y=x3$13x1+

=x3$11x$2 $)$$$$$$$$$$$$$$$$$$$$$$$$$$= $2x2

0 ( 2 12

0= $3.2! $.25 an% 3.35

. a) x=$2 y=15 x=3 y=$5



b) "raph

c) i) y=1.,5ii) x=$1.5

1e)

y=$12x$5

x=$3.! an% 2.,5

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MODULE 10-Graphs of Functions