Pretest
#2 - Ch 2.3-2.6, 3.1, 3.2, 6.1-6.4
1. Given
f(x) = 
, g(x) = 2x - 3
find
a. (f –
g)(x) (3 pts) b. (gf)(x) (3 pts.) c.
(f(g(x)) (4 pts.)
2. Given
the graph of f(x) =| x |
a) Sketch
the graph: y = | x + 2 | - 1 (6 points)
b) Find the
domain and range. (2 points each)
3. Sketch
the graph : (5 points each)
a) 
b) 
4. Given
f(x) = 
a) Find the
inverse of f(x). (5 points)
b) Graph
f(x) and 
on the same set of
coordinate axes (5 points).
5. a) Find two coterminal angles (one
positive and one negative) of 
(5 points).
b) Find the
radius of the circle if the central angle is 
and the arc length is 8.
(5 points)
6. a) Find the six trigonometric functions of the angle 
(in standard position)
whose terminal side passes through (5,-12) (8 points).
b) Find the
tan, sec and cot of if sin = 
and tan > 0 (5 points).
7. a) Evaluate the trigonometric function without using a
calculator. You must show your work.
(5 points)
1. tan 
2. sec
b) Evaluate
using the calculator. Round your answers to four decimal
places. (5 points)
1. sin 2 2.
sec 
8. a) Find
the values of in degrees (0 < < 
) and radians (0 < < 2
) without using a
calculator given sec = -2
(7 points)
b) Find the
values of in degrees (0 < < ) given (5 points)
1. cos = -.7112 2. cot = -2.5678
9. Use the
trigonometric identities to transform one side of the equation to the other. (5
points)
10. Graph
one full period: (5 points each)
a) y = 2cos
(6x) b) y = -sin (2x - )
Answers
1a. 
1b. 
1c. 
2a.
2b. domain:
all real numbers, range: all real numbers greater than or equal -1
3a.
3b.
4a. 
4b.
Note: The solid line is f(x)
and the dashed line is 
.
5a. 
5b. 
6a.
6b.
7a. 7b.1).9093 2) -1.0642
1. 
2. -1
8a.
8b. 1) 
8b. 2) 
9.
10a.
10b.
