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°?

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.

1. a)
2. b)
3. 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.

1. Sketch the graph of the relationship.
2. 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.

1. a)
2. b)

 

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

1. a)
2. b)
3. c)

 

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

4. a) A period of 6 and an amplitude of 4.
5. 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:

1. f(4)
2. b)  f(5)
3. c)  f(8)
4. 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

1. a) f(43)
2. b) f(79)
3. c) f(-1)

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

1. a) Plot a graph of temperatures versus dates. Draw a periodic function that represents the data as accurately as possible.
2. 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 :

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