107 Math Test 1 Chapters 8 & 9
Printed Name:
Calculators are allowed on this test...neighbors are not ! Show work for credit.
1
Use the graph below to answer the following questions.
A
fx
1
5 pts
What is f (1).
..................................................................................
1
2
3
x
1
B
2
5 pts
If f (x) = 2, nd x.
..................................................................................
3
C
6 pts
What is the range of f ?
...........................................................................................................................
D
6 pts
Find 3f (3) + 1
............................................................................................................................
E
7 pts
Sketch the graph of y = f (x 2) + 1. Label at least 3 points.
y
2
1
3
2
1
1
2
3
4
5
x
1
2
3
4
5
............................................................................................................................
F
6 pts
Dr. Emmert Fall 2010
What is the domain of y = f (x 2) + 1.
I of III
Points Earned
of 35
Math 107 Test 1 Chapters 8 & 9
Let r(x) = x2 5 and k (x) = x + 1.
2
A
6 pts
Find (r k )(x).
............................................................................................................................
B
4 pts
Are the functions r and k inverses?
Yes
3
8 pts
No
Let H (x) = (x2 5)3 + 7. Find two functions, f and g such that H (x) = (f g )(x).
f (x) =
g ( x) =
4
8 pts
Let b(x) = x3 5. Find the inverse function of b.
5
5 pts
5x2 + 3x + 3 = 0 Classify the solutions of this equation. If there is no real solution, please state No Real
Solution.
Points Earned
of 31
II of III
Dr. Emmert Fall 2010
Math 107 Test 1 Chapters 8 & 9
6
Let N = f (T ) give the number of it days takes a certain kind of insect to develop as a function of the
temperature T (in C ). At 45 C the maximum it can toleratethe insect requires 10 full days to develop. An
additional day is required for every 2 C drop, and it cannot develop in temperatures below 5 C .
Days
30
A
6 pts
What is the domain of this function?
..........................................................................
25
20
15
B
6 pts
What is the range of this function?
10
..........................................................................
5
5
7
10
15
20
25
30
35
40
45
T
C
8 pts
Graph the function. Label at least two points.
If a diver jumps o a diving board that is 6 feet above the water at a velocity of 20 feet per second, his height,
h, in feet above the water can be modeled by h(t) = 16t2 + 20t + 6 where t 0 is in seconds.
A
7 pts
How long is the diver in the air before he hits the water?
.............................................................................................................
B
7 pts
Dr. Emmert Fall 2010
What is the maximum height achieved?
III of III
Points Earned
of 34
fx
1
2
3
x
1
2
3
2
1
3
2
1
Domain: All Real except x 0
Range: All Real except y 0
3
x
1
1
1
2
Domain: All Real
1
Range: y 3
2
3
fx
4
3
3
1
3
2
1
fx
3
1
1
2
3
x2
4
x
1
2
Domain: All Real except x
Range: y 0 1
2
2
1
0
2
2
1
1
2
3
3
fx
2
1
1.0
0.5
0.5
1.0
1.5
2.0
fx
Domain: All Real
Range: All Real
1
x
x
2
1
2
Domain: x 0
Range: y 0
3
3
1
3
2
2
1
1
2
3
4
fx
Library of Functions
1
1
1
1
2
3
fx
1
2
2
Domain: All Real
Range: y 0
x
Domain: All Real
Range: y 0
x2
3
2
2
x3
1
1
5
5
2
1
1
fx
2
1
1
x
2
2
Domain: All Real
Range: All Integers
Domain: All Real
Range: All Real
fx
3