Name: ________________________ Class: ___________________ Date: __________
Pre-AP Algebra II Review of CBA-1 (Ch. #1)
Each question is equally weighted. (15 questions x 10 points each=150 Points Max)
1
Consider the graph of the function f (x) 
1
.
x1
Which of the following is a TRUE statement based on the graph?
A)
B)
C)
D)
The domain is all real numbers:   x  
The range is all real numbers:   y  
The graph does not have any x- or y-intercepts.
The maximum value of the function on the interval [2, 5] is 1.
2
2
Find an equation for the inverse of the function f (x) 
3
3
x  , and graph the inverse on the
5
2
coordinate plane.
F)
f
G)
f
1
1
(x) 
5
5
x
3
2
H)
f
(x) 
5
5
x
3
2
J)
f
2
1
5
5
(x)   x 
2
3
1
5
5
(x)   x 
2
3
3
Graph the linear function f (x)  3x  3 and find the intercepts.
A)
C)
x-intercept: (–1, 0)
y-intercept: (0, – 3)
x-intercept: (1, 0)
y-intercept: (0, – 3)
D)
B)
x-intercept: (–1, 0)
y-intercept: (0, 3)
x-intercept: (1, 0)
y-intercept: (0, 3)
3
4
Graph the linear function f (x)  3x  3 and find the intercepts.
F)
H)
x-intercept: (1, 0)
y-intercept: (0, + 3)
x-intercept: (–1, 0)
y-intercept: (0, + 3)
J)
G)
x-intercept: (1, 0)
y-intercept: (0, –3)
x-intercept: (–1, 0)
y-intercept: (0, –3)
4
5
3
Consider the graph of the function f (x)  x  2.
Which of the following is a FALSE statement based on the graph?
A)
B)
C)
D)
The domain is all real numbers:   x  
The range is all real numbers:   y  
The maximum value of the function on the interval [-1, 1] is -1.
The graph has a y-intercepts at (0, 2).
Free Response: Please show all your work. You may get a partial credit even if you cannot find the correct answer.
6
Let f(x)  6x  4 and g(x)  5x  7. Find f  g and its domain and range.
7
Let f(x)  4x  5 and g( x)  7x  3. Find f  g and its domain and range.
5
8
Let f(x)  x 2  3 and g(x) 
x 2
. Find ÊÁË g û f ˆ˜¯ (2) .
3x
9
Let f(x)  x 3  5 and g(x) 
x 3
. Find ÊÁË g û f ˆ˜¯ (2) .
x
10
11
Find the inverse of the function f (x) 
Find the inverse of the function f (x) 
2
2(x  1)  3
4
2
(x  4)  2
3
6
.
1
12
Use composition of functions to explain whether f (x ) 
5(x  2)
3
x  2 and g (x ) 
are inverse
5
3
functions. Show your work.
13
Make a mapping diagram for the relation:
{(–1, 2), (0, 1), (3, –3), (6, 3)}
14
Make a mapping diagram for the relation:
{(–3, –1), (–1, –5), (0, 4), (3, –6)}
15
Let f(x)  x 2  4 and g(x)  x  2. Find
16
Let f(x)  x 2  16 and g(x)  x  4. Find
17
Find the inverse of the function f (x) 
2
x  2.
3
18
Find the inverse of the function f (x) 
3
x  3.
8
f
and its domain and range.
g
f
g
7
and its domain and range.
19
Let f(x)  x  5 and g(x)  x 2 . Find ÊÁË g û f ˆ˜¯ (1) .
20
Let f(x)  x  4 and g(x)  x 2 . Find ÊÁË g û f ˆ˜¯ (5) .
21
ÏÔ Ê
¸
Ô ÁÁ
1 ˆ˜˜ ÊÁÁ 1 ˆ˜˜ ÊÁÁ 3 ˆ˜˜ ÊÁÁ 2 ˆ˜˜ ÔÔ
Find the domain and range of the relation: ÌÔ ÁÁ 1, ˜˜ , ÁÁ  , 1 ˜˜ , ÁÁ , 0 ˜˜ , ÁÁ 2, ˜˜ ˝Ô
2 ¯ Ë 2 ¯ Ë 2 ¯ Ë 3 ¯ Ô˛
ÔÓ Ë
22
ÔÏÔ
ÊÁ 1 ˆ˜ ÊÁ 1 ˆ˜ ÊÁ 2 ˆ˜ Ô¸Ô
Find the domain and range of the relation: ÌÔ (1, 3), ÁÁÁ  , 3 ˜˜˜ , ÁÁÁ , 0 ˜˜˜ , ÁÁÁ 2, ˜˜˜ ˝Ô
ÔÓ
Ë 2 ¯ Ë 2 ¯ Ë 5 ¯ Ô˛
23
A bucket has 12 inches of water in it but there is a hole in the bottom. Use interval notation to write
the domain and range of the function H (x)  12  1.5x, where x is the time the water has been leaking
for (in minutes) and H (x) is the height of the water (in inches).
24
A man has to travel 20 miles. His displacement during the time is demonstrated by the function
D (x)  20  5x, where x is the time (in hours) and D (x) is the distance travelled (in miles). Find the
domain and range of this function
25
2
Let f (x)  4x  3 and g (x)  x  2x  3. What is f  g ?
26
2
Let f (x)  2x  1 and g (x)  x  3x  3. What is f  g ?
8