Relations, Functions and Graphs Quiz #1
Question 1
Draw the graph of the following relations using suitable scales.
(i) x = 4 (iii) y = -5
(ii) x = 2.5 (iv) y = 6
Solutions:
(i)
(ii)
(iii)
(iv)
Question 2
Draw the graphs of the linear functions:
(i) f(x) = 2x + 3
(ii) f(x) = 6x
for the domain -1 ≤ x ≤ 2.
Solutions:
(i) Substitute the values given for x in the domain (-1, 0, 1, 2), in the function, solving for the respective f(x)/y values.
Given, f(x) = 2x + 3
f(-1) = 2(-1) + 3 = -2 + 3 = 1
f(0) = 2(0) + 3 = 0 + 3 = 3
f(1) = 2(1) + 3 = 2 + 3 = 5
f(2) = 2(2) + 3 = 4 + 3 = 7
Therefore, the set of (x, y) values to be plotted and connected in forming the linear function are:
{(-1, 1), (0, 3), (1, 5), (2, 7)}.
(ii) Substitute the values given for x in the domain (-1, 0, 1, 2), in the function, solving for the respective f(x)/y values.
Given, f(x) = 6x
f(-1) = 6(-1) = -6
f(0) = 6(0) = 0
f(1) = 6(1) = 6
f(2) = 6(2) = 12
Therefore, the set of (x, y) values to be plotted and connected in forming the linear function are:
{(-1, -6), (0, 0), (1, 6), (2, 12)}.
Question 3
Find the equation of the line which passes through the points A (2, 4) and B (8, 10).
Solution:
Using the equation of a straight line:
y = mx + c
Substituting (2, 4) for x and y respectively
4 = m(2) + c
4 = 2m + c —- eq(1)
Substituting (8, 10) for x and y respectively
10 = m(8) + c
10 = 8m + c—- eq(2)
eq(2) – eq(1)
10 – 4 = 8m – 2m + c – c
6 = 6m
m = 1
Substituting m = 1 in eq(1)
4 = 2m + c
4 = 2(1) + c
4 = 2 + c
c = 4 – 2
c = 2
Hence the equation of the line passing through points A (2, 4) and B (8, 10) is:
y = mx + c
y = (1)x + (2)
y = x + 2
Question 4
The data below are the sizes (to the nearest inch) of the waists of 30 students in a class.
20 21 23 25 26 27
20 21 23 26 26 27
20 22 23 26 26 27
21 22 24 26 27 28
21 22 24 26 27 28
(a) Copy and complete the frequency table below.
| Size of Waist (Inch) | Frequency |
| 20 | ____ |
| 21 | 4 |
| 22 | ____ |
| 23 | 3 |
| ____ | 2 |
| 25 | ____ |
| 26 | ____ |
| ____ | 5 |
| 28 | 2 |
(b) Draw a Frequency Polygon for the information presented above.
Solutions:
(a)
| Size of Waist (Inch) | Frequency |
| 20 | 3 |
| 21 | 4 |
| 22 | 3 |
| 23 | 3 |
| 24 | 2 |
| 25 | 1 |
| 26 | 7 |
| 27 | 5 |
| 28 | 2 |
(b)
