**Unité 2: La représentation de fonctions**

*Travail formatif 2.1 (Section 1 et 2)*

**Section 1:**Comparison of functions.**Section 2:**Graphs of sine and cosine functions.

**Question 1:** Sketch the following functions and then determine the domain, image, y-intercept, x-intercept, and whether it is an increasing or decreasing function.

- a)
- b)
- c)

**Question 2: ** The chess club is holding a bake sale one lunchtime a week to raise money for the end-of-year trip to Stratford. If the chess club sells 65 baked goods per week, the club makes a profit of $3 per baked good. By reducing the profit by $0.5 per baked good, the chess club can sell 20 more baked goods per week. The equation represents the relationship between profit per bakery per week and the number of $0.5 discounts.

- Sketch the graph of the relationship.
- Determine the domain, image, y-intercept, x-intercept, and whether it is an increasing or decreasing function.

**Question 3: ** Indicate whether the graph is periodic or non-periodic. Justify your decision.

- a)
- b)

**Question 4: ** Determine the period and amplitude of the functions below.

- a)
- b)
- c)

**Question 5:** Sketch a graph of a periodic function with the period and amplitude shown.

- a) A period of 6 and an amplitude of 4.
- b) A period of 3 and an amplitude of 5.

**Question 6 : **Answer sub questions 1) to 3) about the periodic function shown here.

- Describe how you would determine the period of the function.
- Describe how you would determine:

- f(4)
- b) f(5)
- c) f(8)
- d) f(13)

- Describe how you would determine the magnitude of the function.

**Question 7:**

The period of a function, f(x), is 12. If f(7) = -2 and f(11) = 9, find the value of

- a) f(43)
- b) f(79)
- c) f(-1)

**Question 8:** Mid-season maximum temperatures were recorded for three years in Dorset, Ontario. The results are shown here.

- a) Plot a graph of temperatures versus dates. Draw a periodic function that represents the data as accurately as possible.
- b) Use the graph to approximate the period and amplitude of the function.

Season |
Date |
Température (C) |

Winter | 5 février 1998 | -9 |

Spring | 2 mai 1998 | 16 |

Summer | 3 août 1998 | 25 |

Fall | 2 novembre 1998 | 3 |

Winter | 5 février 1999 | -10 |

Spring | 2 mai 1999 | 17 |

Summer | 3 août 1999 | 27 |

Fall | 2 novembre 1999 | 3 |

Winter | 5 février 2000 | -10 |

Spring | 2 mai 2000 | 16 |

Summer | 3 août 2000 | 26 |

Fall | 2 novembre 2000 | 3 |

** Question 9** :

- Draw the graph y = tan x in the Cartesian plane below.
- Indicate if the representation is a function. Justify.
- Is the function periodic? If yes, what is the period?
- How does the graph y = tan x evolve when x goes from 0° to 90° and from 90° to 270°?
- What is the value of tan x when x = 90° and when x = 270°?
- What is the maximum value of y?
- Quelle est la valeur minimale de y?
- What is the y-intercept?
- What are the abscissae at the origin?
- Determine the domain and image of the function.