REVIEW ASSIGNMENT
TRANSFORMATIONS
ANSWER KEY
Name: _________________________________________
Teacher:________________________________________
School:_________________________________________
Total ______ = _________%
51
Page 1 of 10
1. For the function y = f ( x ) graphed below. Sketch each function on the grid provided.
For each graph: a) explain what change(s) you made to y = f ( x ) .
b) Give the new coordinates of the point provided in each question.
(4 marks for each, 2 marks for graph)
5 5
1
a) y = f x
2
5
horizontal expansion by a factor of 2
______________________________________
______________________________________ 5 5
( 4, 2 ) (8, 2 )
________________
5
Page 2 of 10
1
b) y=− f ( x)
2
reflection over the x - axis
_______________________________________ 5
1
vertical compression by a factor of
2
_______________________________________
5 5
( 2, − 2 ) ( 2, 1)
________________
c) x = f ( y)
reflection in the line y = x
__________________________________
5
__________________________________
( −3, 0 ) ( 0, −3)
_______________
5 5
Page 3 of 10
d) y = f ( 2x − 6) + 4 y = f ( 2 x − 3) + 4
1
horizontal compression by a factor of
___________________________________ 2 5
translate 3 units right and 4 units up
___________________________________
( 4, 2 ) ( 5, 6 ) 5 5
______________
2. Given the graph of y = f ( x ) , on the same grid sketch the graph of y = − 2 f ( 3x )
5 5
3 marks
Page 4 of 10
3. Given the graph of the function y = f ( x ) below, sketch the graph of 2 y = f ( 3x − 6 ) − 2 on the grid
provided.
5 5
5 5 5 5
5 5
3 marks
4. Two functions are graphed below. y = f ( x ) and y = f ( a ( x − b ) ) . Determine the values of a and b .
y = f ( a ( x − b))
y y
y = f ( x)
5 5
x x
−5 5 −5 5
−5 −5
a = − 1, b = − 3
4. ________________________
2 marks
Page 5 of 10
5. The graph of y = f ( x ) is shown below. The sketches of transformations of f ( x ) are given in the
following graphs. Write an equation in terms of f ( x ) to represent the graphs of the transformations.
x
−5 5
−5
a) y
x
−5 5
y = f ( x − 4) − 2
−5
or
y + 2 = f ( x − 4)
a) _____________________
2 marks
Page 6 of 10
b) y
x
−5 5
y = 2 f (−x)
or
−5
1
y = f (−x)
2
b) _____________________
2 marks
c) y
x
−5
y = f ( 2 ( x + 4))
5
or
−5
y = f ( 2 x + 8)
c) _____________________
2 marks
6. Write the equation of the transformed function 𝑦 = 𝑥 2 after the following transformations
in the order given.
1
a) A vertical compression by a factor of followed by a transformation of 3 units right.
3
3 y = ( x − 3)
2
or
1
y = ( x − 3)
2
3
a) ___________________________
2 marks
Page 7 of 10
1
b) A horizontal compression by a factor of , then a reflection in the y -axis followed
4
by 2 units down.
y + 2 = 16 x 2
or
y = 16 x 2 − 2
b) ___________________________
2 marks
c) A horizontal expansion by a factor of 6 followed by a translation of 4 units left and 5 units up.
2
1
𝑦 − 5 = ( [𝑥 + 4])
6
𝑜𝑟
2
1
𝑦 = ( [𝑥 + 4]) + 5
6
c) ___________________________
2 marks
7. The graph of y = 16 − x 2 has the following transformation applied to it. Determine an
equation for the new graph.
1
a) a horizontal compression by a factor of .
2
y = 16 − 4 x 2
a) ___________________________
2 marks
Page 8 of 10
b) a vertical expansion by a factor of 3, then reflected in the y -axis.
1
y = 16 − x 2
3
or
y = 3 16 − x 2
b) ___________________________
2 marks
2−x −1
8. If f ( x ) = , determine the equation of f ( x ) , the inverse of f ( x ) .
5x
2
y =
5x + 1
8.____________________________
3 marks
Page 9 of 10
9. For the function y = f ( x ) graphed below, list all the coordinates of the INVARIANT points for the
following transformations. Hint: Invariant points do not move when a transformation is applied.
a) y = f ( − x )
b) y = − f ( x )
c) x = f ( y) 5
5 5
( 0, 1)
a) ___________________________
2 marks
( −2, 0 ) , ( 2, 0 )
b) ___________________________
2 marks
(1, 1)
c) ___________________________
2 marks
10. The point (8, − 5) is on the graph of y = f ( x ) , which point must be on the graph
3
of y = + 5?
f ( − x + 1) − 2
38
−7,
7
10. ___________________________
2 marks
Page 10 of 10
