MCR 3U1 – Unit 1: Functions and Relations
NAME: ______________________
DATE: ______________________
KN:
AP:
TH:
CM:
/20
/17
/12
/18
KNOWLEDGE – PART B (5 marks)
1. If f ( x)  2 x 2  7 x  10 , find the following: (5 marks – 3, 2)
a) f ( x  1)
b) x, if f ( x)  5
APPLICATION (17 marks)
2. The relationship between the measure of an interior angle, a, in degrees , of a polygon and its number of
sides, n, can be modeled by the function.
360
a (n)  180 
n
a) Determine the inverse of the function. (2 marks)
b) What does the inverse function represent? (1 mark)
c)
State the domain and range of the function and its inverse. (2 marks)
d) If an interior angle measures 45o, how many sides does the polygon have? (2 marks)
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MCR 3U1 – Unit 1: Functions and Relations
1
3. Graph g ( x)  2   1  3 and graph the parent function on the grid below. Label your graph fully.
3
Include your transformation statement and table of values. (6 marks)
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MCR 3U1 – Unit 1: Functions and Relations
4. Let f ( x)  3x  1 and g ( x)  2  x . Determine the values of a such that f (a 2 )  g (2a) . (4 marks)
THINKING (12 marks)
5. a) Using proper function notation, express the area, A, of the shaded region of the following figure as a
function of r. (3 marks)
1
r
b) State the domain and range of the function you created in a). (2 marks)
6. Given f ( x)  x 2  x  6 , determine the x-intercepts for y  f (3 x) . (3 marks)
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MCR 3U1 – Unit 1: Functions and Relations
7. Given
, find the value of k if
1. (4 marks)
COMMUNICATION (18 marks)
8. List all the transformations from the graph of y  f (x). Be specific! (3 marks each)
a) y  0.5 f ( x  1)  5
b) y  3 f (3x  3)
9. State the equation of each graph below. (2 marks each)
a) y  x
Equation: _______________
b) y 
1
Equation: _______________
x
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MCR 3U1 – Unit 1: Functions and Relations
5. Find the equation of each of the following functions after the given transformation(s). (4 Marks)
a) y  x
is stretched horizontally by a factor of 3, reflected in the y-axis, and translated 2 units left and
1 unit up.
b) The graph of y  x is compressed vertically by a factor of
1
, reflected in the y-axis, and translated 5
3
units left and 1 unit down.
Overall Math Form
Level 1
(1 mark)
Level 2
(2 marks)
Level 3
(3 marks)
Level 4
(4 marks)
Uses Mathematical
language, symbols, visuals,
and conventions correctly.
Rarely
Sometimes
Usually
Always
Congratulations! This is the end of the Unit Test.
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