Form 5 Chapter 2 Graphs of Functions II

1 (a) Complete the table below for the equation y=−12x

by writing down the values of y when x = - 2

and x = 2.5 [2 marks]

(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 the x -axis and 2 cm to 5 units on the y -axis, draw the graph of

y=−12

x for -4 ≤ x ≤ 4. [4 marks]

(c) From your graph, find : the values of y when x = -1.5 the values of x when y = -5 [2 marks]

(d) Draw a suitable straight line on your graph to find the values of x which satisfy the equation −x2+4 x = - 12 for -4 ≤ x ≤ 4. State the value of x. [4 marks]

2. (a) Complete the table below for the equation y=10x

by writing down the values of y when x = - 0.5

and x = 2.5 [2 marks]

(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 the x -axis and 2 cm to 5 units on the y -axis, draw the graph of

y=10x

for -4 ≤ x ≤ 4. [4 marks]

(c) From your graph, find : the values of y when x = -2.5 the values of x when y = -1.5 [2 marks]

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

10x

+4 x = - 12 for -4 ≤ x ≤ 4. State the value of x. [4 marks]

Prepared: William Teo

2011 Page 1

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

y 3 12 24 -24 -12 -6 -3

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

y -2.5 -5 -10 20 10 5 2.5

3. (a) Complete the table below for the equation y=x3−12 x+10 by writing down the values of y when x = - 3 , x = -1 and x = 3 [2 marks]

(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 the x -axis and 2 cm to 5 units on the y -axis, draw the graph of

y=x3−12 x+10 for -4 ≤ x ≤ 4. [4 marks]

(c) From your graph, find : the values of y when x = 0.5 the values of x when y = 18 [2 marks]

(d) Draw a suitable straight line on your graph to find the values of x which satisfy the equation x3−10 x+2 = 0 for -4 ≤ x ≤ 4. State the value of x. [4 marks]

4. (a) Complete the table below for the equation y=− x3+10 x−3 by writing down the values of y when x = - 2 and x = 3 [2 marks]

(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 the x -axis and 2 cm to 5 units on the y -axis, draw the graph of y=− x3+10 x−3 for -4 ≤ x ≤ 4. [4 marks]

(c) From your graph, find : the values of y when x = -2.5 the values of x when y = 5 [2 marks]

(d) Draw a suitable straight line on your graph to find the values of x which satisfy the equation x3−10 x+2 = 0 for -4 ≤ x ≤ 4. State the value of x. [4 marks]

Prepared: William Teo

2011 Page 2

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

y -6 26 10 -1 -6 26

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

y 21 -6 -11 -3 6 0 26