Math 124 Problems-Worksheet 1
EXPONENTIAL FUNCTIONS
1) When the Olympic games were held outside Mexico City in 1968, there was
much discussion about the effect the high altitude (7340 feet) would have on the
athletes. Assuming air pressure decays by 0.4% every 100 feet, by what
percentage is air pressure reduced by moving from sea level to Mexico City?
2) Find a formula
Contains the points (-2,0.48) and (2,18.75)
50
40
30
20
10
0
-2
-1
0
1
2
3
x
INVERTIBLE FUNCTIONS
1. In each case, explain or verify that the given function is invertible. Find the inverse
function.
A.
m
f (m)
B.
1
2
3
4
5
0.09 2.10 5.60 7.80 9.40
S (t )  At 3  K where A and K are constants.
C.
G(x)
5
x
0
0
10
2. The life expectancy, L , of a child can be expressed as a function of the year of birth,
y.
y  66.94
where y  0 corresponds to 1950. Use the graph of L ( y ) to
L( y ) 
0.01y  1
estimate L1 (76) .
Include a practical interpretation of your answer.
TRANSFORMATIONS
Use the numerical representation of f ( x) below to match the numerical information in
column A with the symbolic representation in column B.
x
f ( x)
Column A
-4
5
-2
1
0
6
1.
x
g ( x)
a.
-4
7
-2
3
0
8
2
4
-2
5
-1
1
0
6
1
2
2
7
c. f ( x)  2
-2
5
0
1
2
6
4
2
6
7
d. f ( x)
4.
x
n( x )
-8
5
-4
1
0
6
4
2
8
7
5.
x
l ( x)
e
-4
-5
-2
-1
0
-6
2
-2
f.  f ( x)
4
5
2
1
0
6
-2
2
-4
7
g. f ( x  2)
7.
x
u ( x)
f ( x  3)  4
4
-7
6.
x
k ( x)
f ( x  2)
1 
b. f  x 
2 
3.
x
m( x )
4
7
4
9
2.
x
h( x )
2
2
Column B
7
11
5
6
3
10
1
5
-1
9
h.
f (2 x)
LOGARITHMS
1)Solve for x
a) 50=600
b)
e0.4 x
9  2e
x
x2
2)Put the function in form
P  PO e kt
P  4(0.55)t
3)The population of a region is growing exponentially. There were 40x106 people in
1980(t=0) and 56x106 in 1990. Find an expression for the population at time t , in years.
What population would you predict for the year 2000? What is the doubling time?
TRIGONOMETRY
1. Consider the standard sine function. What is the period, amplitude, and average value?
2. Consider the transformation y  A  sin( Bx  C )  D where A, B, C , and D are positive
constants.
Explain how the value of these constants affects the graph of the standard sine function.
3. The following function describes the relationship between air temperature in Fairbanks,
Alaska as a
function of time. (National Weather Service).
 2

T (t )  37 sin 
 t  1.7386   25
 365

A. Without graphing this function, determine its period, amplitude, and average
value.
B. Graph one period of this function. Label appropriate values on the axes.
T
t
3. The rate of intake during a respiratory cycle (liters/sec) for a person at rest is
proportional to a
sine wave with period six seconds. Suppose the rate is 0.85 liters/sec when t  1.5 sec.
A. Find an equation that describes the rate of intake as a function of time.
B. Graph one cycle of your equation. Which part corresponds to inhaling?
Exhaling? Explain.
4. Sketch each angle in standard position. Find the exact value if possible.
  
B. tan 

 6 
 3 
A. cos  
 4 
C. sin(2)
5. An angle A is drawn in standard position and its terminal side is in quadrant III. If
3
tan A  ,
5
find values for sin A and sin(2 A) .
6. Solve for t :
tan(3t )  1 where 0  t 

2
.
7. Find exact values for each:
A. cos1 (1)
 1 
B. sin 1  
 2 
8. Simplify each (your answer will be in terms of x ):
A. cos  tan 1 x 
B. sin 1  sin x 