MHF4U: Advanced Functions Name: ___________________________
Unit 1: Characteristics and Properties of Functions Test
__ __
Knowledge Application Thinking Communication
21 12 Level Level
KNOWLEDGE
1) The function 𝑓(𝑥) = |𝑥| has undergone the following transformations.
- Vertical compression by a factor of ½ - Horizontal compression by a factor of ⅓
- Reflection in the x-axis - Horizontal translation right by 5 units
- Vertical translation 3 units downwards
a. Write the transformation using the mapping notation. [ /4]
b. State the equation for the transformed function. [ /4]
g(x) =
c. Apply the transformations to 4 KEY points on f(x). [ /2]
d. On the grid to the right, sketch the functions f(x) and g(x).
[ /2]
e. State the domain and range of g(x). [ /2]
MHF4U: Advanced Functions Name: ___________________________
2) The function given in each graph below is f(x). Sketch the
graph of
a) 𝑦 = 𝑓 −1 (𝑥) [ /2]
b) Is the inverse a function? Explain. [ /2]
3) A function is defined by:
3𝑥 + 1, 𝑥 ≤ −1
𝑓(𝑥) = {
2 − 𝑥 2 , 𝑥 > −1
Graph f(x). [ /3]
APPLICATION
4) Given𝑓(𝑥) = 2𝑥 2 − 3𝑥 + 1 and 𝑔(𝑥) = 5 − 2𝑥, evaluate 𝑔−1 (−3) − 𝑓(𝑎 + 4). [ /3]
MHF4U: Advanced Functions Name: ___________________________
5) For a fundraising event, a local charity organization expects to receive $15,000 from cooperate
sponsorship, plus $30 from each person who attends the event.
a) Use the function notation to express the total income from the event as a function of the
number of people who attend. [ /2]
b) Suggest a reasonable domain and range for the function in part (a).
Explain your reasoning. [ /2]
6) A farmer has 90 m of fencing to enclose a rectangular area and divide it into two sections as shown.
a) Write an equation to express the total area enclosed as a function of the width. [/3]
b) Determine the domain and range of this area function. [ /2]
MHF4U: Advanced Functions Name: ___________________________
THINKING
7. A function f(x) has domain {x R x −4} and range { y R y −1} .
Determine the domain and range of the function y = 3 f (2 x + 2) + 4 .
Thinking Rubric:
Criteria Level One Level Two Level Three Level Four
Use of uses critical/ creative uses critical/ creative uses critical/ creative uses critical/ creative
critical/creative thinking processes thinking processes thinking processes thinking processes with a
thinking processes with limited with some with considerable high degree of
(e.g., problem effectiveness effectiveness effectiveness effectiveness
solving, inquiry)
Communication Rubric:
Criteria Level One Level Two Level Three Level Four
Consistently and
Using correct
Sometimes uses Usually uses Consistently uses meticulously uses
mathematical
mathematical mathematical mathematical mathematical symbols,
symbols, labels,
symbols, labels and symbols, labels and symbols, labels, and labels and conventions,
units and
conventions correctly conventions correctly conventions correctly recognizing novel
conventions
opportunities for their use
