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.