### 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)