# Graph of Functions, Long Questions (Question 1)

Question 1:
(a) The following table shows the corresponding values of x and y for the equation $y=\frac{24}{x}$

 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  $y=\frac{24}{x}$  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)

(b)

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

(d)

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