Chapter One Take Home
Name _________________
Make sure that you know how to do these problems with and without a calculator.
Evaluate the trigonometric functions:
1.
sin
3
 _______
4
3.
2.
tan
11
 _____
6
4. csc
cos
13
 _____
3
25
 _____
4
Sketch a right triangle corresponding to the trigonometric function of the acute angle  .
5. Given cos  
5
, find cot   _____ .
7
6. Solve the equation: 0  x  2 
ii. 2sin 2 x  2  0
i. 2sin 2 x  2  cos x
7. Determine all missing angles and sides for the following oblique triangles:
i.
a  55
b  25
c  72
A  _____
B  _____
C  _____
8. Determine the area of the following triangles:
a  11
b  14
c  20
i.
(Hint: Use Heron’s Formula)
A =______________
ii.
B  130
A = _______________
a  62
c  20
Chapter 1 Section 1
2. The graphs of f and g are given
a) State the values of f  4  and g  3 : ______
b) For what values of x is f  x   g  x  ? _______
c) Estimate the solution of the equation f  x   1 : ______
d) On what interval is f decreasing? _______
e) State the domain and range of f . D: ______ R: _______
f)
State the domain and range of g . D: ______ R: _______
21. If f  x   3x2  x  2 find:
b) 2 f  a 
a) f  2 
Evaluate the difference quotient and simplify your answer.
f  3  h   f  3
h
23. f  x   4  3x  x ,
2
26. f  x  
f  x   f 1
x 1
x3
,
x 1
31. Find the domain of h  x  
1
4
x2  5x
c) f  a  h 
44. Find the domain and sketch the graph of the function.
 x  9 if x  3


f  x   2 x if x  3 
6
if x  3 

64. A function f has domain  5,5 and a portion of its graph is shown.
a) Complete the graph of f if it is known that f is even.
b) Complete the graph of f if it is known that f is odd.
Chapter 1 Section 2 (Use graphing calculator)
23. The table gives the winning heights for the Olympic pole vault competitions in the 20th century.
Year
1900
1904
1908
1912
1920
1924
1928
1932
1936
1948
1952
Height (ft)
10.83
11.48
12.17
12.96
13.42
12.96
13.77
14.15
14.27
14.10
14.92
Year
1956
1960
1964
1968
1972
1976
1980
1984
1988
1992
1996
Height (ft)
14.96
15.42
16.73
17.71
18.04
18.04
18.96
18.85
19.77
19.02
19.42
a) Make a scatter plot and decide whether a linear model is appropriate.
b) Find and graph the regression line.
c) Use the linear model to predict the height of winning pole vault at the 2000 Olympics and compare with
the actual winning height of 19.36 ft.
d) Is it reasonable to use the model to predict the winning height at the 2100 Olympics?
Chapter 1 Section 3
The graph of f is given. Draw the graphs of the following functions.
4. a) y  f  x  4 
d) y  
5. a) y  f  2 x 
d) y   f   x 
40. Find f
g h
f  x   tan x
g  x 
x
x 1
h x  3 x
1
f  x  3
2
50. Use the table to evaluate each expression.
1 2 3 4 5 6
x
f  x 3 1 4 2 2 5
g  x

b) g f 1

6
3
2
1
2
3

d) g g 1

f)
f
g  6 
51. Use the graph to evaluate each expression.

b) g f  0

d)
g
f  6 
f)
f
f  4
Chapter 1 Section 5 (Use a graphing calculator)
28. The table gives the population of the United States, in millions, for the years 1900-2000. Use a graphing
calculator with exponential regression capability to model the US population in 1900. Use the model to estimate
the population in 1925 and to predict the population in 2020.
Year Population
Year Population
1900 76
1960 179
1910 92
1970 203
1920 106
1980 227
1930 123
1990 250
1940 131
2000 281
1950 150
Chapter 1 Section 6
 
 , where 1  x  1
2
16. Let f  x   3  x 2  tan 
a) Find f 1  3
23. Find the formula for the inverse of f  x   e x

b) Find f f 1  5 
3
59. Find the exact value of each equation.
3
2
a) sin 1  
b) cos
1
 1
