Graph of Functions, Long Questions (Question 1)


Question 1:
(a) The following table shows the corresponding values of x and y for the equation y= 24 x
  
x
–4
–3
–2
–1
1
1.5
2
3
4
y
–6
k
–12
–24
24
n
12
8
6
Calculate the value of k and n.

(b) For this part of the question, use graph paper. You may use a flexible curve rule.
By using a scale of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph of  y= 24 x  for –4 ≤ x ≤ 4.

(c) From your graph, find
(i) The value of y when x = 3.5,
(ii) The value of x when y = –17.

(d) Draw a suitable straight line on your graph to find the value of x which satisfy the equation 2x2 + 5x = 24 for –4 ≤ x ≤ 4.

Solution:
(a)
y= 24 x when x=3, k= 24 3 =8 when x=1.5, n= 24 1.5 =16

(b)


(c)
(i) From the graph, when x = 3.5, y = 7
(ii) From the graph, when y = –17, x = –1.4

(d) 
              y= 24 x  -------------- (1)              2 x 2 +5x=24 ------ (2) (2)÷x, 2x+5= 24 x  -------- (3) (1)(3), y(2x+5)=0                y=2x+5

The suitable straight line is y = 2x + 5.
Determine the x-coordinate of the point of intersection of the curve and the straight line y = 2x + 5.

x
0
3
y = 2x + 5
5
11

From the graph, x = 2.5