1. EXAM I(Practice)
Charles Zhang
Spring 2015
Math 220
Name:_______________________
Show work to get partial credit, and show enough work to get full credit!
1. Find the domain for each of the following functions, and write them in interval forms:
(a) ln( 2)y x 
(b) 2
sin( 2)y x 
(c)
2
1



x
x
y
2. Solve each of the following inequalities and write your answers in interval form:
a. 12537  x
b. 3 7 8x  
3. A line is perpendicular to 2 7 0x y   and passes through (4,6) . Find the equation
for the line.
4. Given ( )
1
x
f x
x


and 2
( )g x x . Calculate the composite functions of g and
og f .
5. Find cos , sec and tan if
1
sin
3
  and  is acute.
6. Solve for 0 2x   :
0cos2sin  xx
7. Express )cos(cot 1
x
in terms of x (where x is any real number).
8. Find the domain (in interval form) on which  
1
3
x
f x
x



is one-to-one and a
formula for the inverse of f .
9. Without using a calculator to determine the value of each of the following:
(a) 1 1
tan cos
2
 
 
 
(b) 





3
2
sinsin 1 
10. Prove  2222
sintansintan 
11. (a)Find the radius of the circle with the centre at ( 2,1) passing through (0,2) .
(b)Set up the equation for the circle given in (a).
12. Determine whether the following functions are even, odd or neither even nor odd:
A) 2
1 sin x

2. B)
1
x
x

C)
2
1
2x 
D) 3 2
1
1x x 
13. Determine each of the following functions is algebraic or transcendental:
A) 2
1 sin x
B)
1
x
x

C)
2
1
2x 
D) 3 2
1
1x x 
14. Convert the given equation 2
2 1y x x    to its standard form by completing the
squares and find the vertex of the parabola, and then graph the parabola.
15. Solve each of the following equations:
a. 062
 xx
ee
b. 1)1ln()1ln(  xx
16. Evaluate 9log7
17. Expand the following into algebraic sum of simple logarithms:








3
3
log
yx
yx
18. Find the graph of 1)1(2  xfy if the graph of )(xfy  is given as follows:
-1 0 1
1