Day 5: Combinations of Transformations
REVIEW: Determine the equation of the functions pictured below.
FUNCTION 1:
1. List the transformations that need to be applied to
2. Graph
to obtain the graph of
and state the function’s domain and range.
FUNCTION 2:
1. List the transformations that need to be applied to
2. Graph
to obtain the graph of
. State the period and any points where y = 0.
.
FUNCTION 3:
1. Graph
. State the domain and range.
2. Identify the period and the amplitude.
FUNCTION 4:
Graph
FUNCTION 5:
. State the domain and range.
Graph
. State the range.
Independent Practice:
1. Graph
.
2. Graph
3. Graph
4. Graph
Example #1:
. State the domain and range.
.
. State the equation of the axis, the amplitude and the range.
The graph above shows a function y = f(x).
Graph the following on the same set of axis: y = 2 f [ -⅔ ( x - 1) + 2 ]
Point
(-4, -3)
(-2, -1)
(0, 1)
(2, 0)
(4, 2)
𝑦 = 𝑎 𝑓 (𝑘 ( 𝑥
− 𝑑))
+ 𝑐
a
b
h
k
11.
–2
–3
–4
–5
12.
4
2
0
0
13.
–1
–1
–1
0
0
–11
horizontal
stretch/compression
and factor
horizontal
translation
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
14.
15.
3
H.S. by
4 left
16.
–4
0
H.C. by ⅙
3 right
17.
1
–2
H.S. by 5
none
Describe how the graph of each of the following functions can be obtained from the graph of y = f(x).
18.
19.
20.
21.
22.
23.
24.
25.
Example #2:
a) Graph f(x) = 3 ( x - 2 )2 + 4
Example #3:
b) Graph f(x) = 2√−0.25𝑥
Example #4:
c) Graph f(x) = −
2
-1
𝑥+5
Example #5:
d) Graph f(x) = ⅓ (3 - x - 2 ) - 4
Example #6:
e) Graph f(x) = - 4 cos (½ x + 30) + 2
Example #7:
f) Determine the equation of the graphs below.