MCR3U1
Transformations: Horizontal, Vertical Translations and Reflections
1. Sketch and label the graphs for each of the indicated functions below.
a)
b)
y
y
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
-7
-6
-5
-4
-3
-2
i) f(x + 3)
-1
1
x
1
-1
2
3
4
5
6
-7
7
-6
-5
-4
-3
-2
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
-8
-8
-9
-9
ii) f(x) – 2
iii) -f(x)
i) f(x+3)+2
c)
x
1
2
3
4
ii) f(x-1)+3
5
6
7
iii) –f(x-4)
d)
y
y
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
-7
-6
-5
-4
i) f(x+3) – 4
-3
-2
-1
-1
1
x
1
2
3
4
5
6
7
-7
-6
-5
-4
-3
-2
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
-8
-8
-9
-9
ii) f(x – 2)+2
i) –f(x+3)
x
1
2
3
4
ii) f(x+6) – 3
5
6
7
2. The function y = f(x) has been transformed to y = f(x – h) + k. Determine the values
of h and k for each of the following transformations.
a) 6 units upward
b) 8 units downward
c) 3 units to the right
d) 5 units to the left
e) 2 units to the left and 4 units downward and reflection about the x-axis
f) 7 units to the right and 7 units upward
g) 4 units to the left and reflection about the x-axis
3. Use transformations to sketch the graph of each of the following functions.
=√ +
a)
b) ( ) =
−
−
y
y
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
-7
-6
-5
-4
-3
-2
-1
1
x
-1
1
2
3
4
5
6
7
-7
-6
-5
-4
-3
-2
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
-8
-8
-9
-9
4. State the equation of the image graph.
a)
x
1
2
3
4
5
6
7
b)
y
y
5
4
4
3
=√
3
2
2
1
1
x
x
-2
-1
1
2
3
4
5
6
7
8
-5
-4
-3
-2
9
1
-1
-1
-2
-1
-2
=
-3
-4
-3
-5
2
3
4
5
MCR3U1
Vertical and Horizontal Translation
Name:
1. For any function y = f(x), explain what happens to y = f(x) if x is replaced by
a) x – 3
c) x 
b) x + 4
1
2
2. For any function y = f(x), state the image if it has the following transformations.
a) vertical shift up by 3 units.
b) Horizontal shift left by 2 units.
c) Horizontal shift right by 1 unit and vertical shift down by 7 units.
3. Sketch the image of the given graph.
a) f(x-2) + 4
-6
-4
b) f(x + 3) + 2
5
5
4
4
3
3
2
2
1
1
-2
2
4
6
-6
-4

-2

-1
2
4
6
-1

-2
-2
-3
-3
-4
-4
-5
-5
c) f(x – 1) – 1
-6
d) f(x – 3) - 2
-4
5
5
4
4
3
3
2
2
1
1
-2
2
4
6
-6
-4
-2
2
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
4
6