Functions #2
Math 122 ESP
Spring 2014
1. The population of a city, P, in millions, is a function of t, the number of years since 1950, so P = f (t).
Explain the meaning of the statement f (35) = 12 in terms of the population of this city.
The statement me
Exam #1 Review
Math 122 ESP
Spring 2014
1. Let f (x) = 3x2 x. Evaluate
(a) f (x + h)
f (x + h) = 3(x + h)2 (x + h)
= 3(x2 + 2xh + h2 ) x h
= 3x2 + 6xh + 3h2 x h
(b) f (x + h) f (x)
f (x + h) f (x) = 3x2 + 6xh + 3h2 x h (3x2 x)
= 3x2 + 6xh + 3h2 x h 3x2 +
Exam #2 Review
Math 122 ESP
1. Let f (x) =
Spring 2014
3
2x+5
(a) Find the inverse of f (x). We solve x = f (y) for y:
3
2y + 5
3
2y + 5 =
x
3
5
y=
2x 2
x=
(b) Show that f (f 1 (x) = x (Check your answer from the previous part). Surprise, you check that
t
Applications of Trigonometry
Math 122 ESP
Spring 2014
1. Show that the exact value of tan(tan1 (1) + tan1 (2) + tan1 (3) = 0. What does this tell you about
the value of
tan1 (1) + tan1 (2) + tan1 (3)
To work this out, we apply the tangent sum of angles fo
Logarithms
Math 122 ESP
Spring 2014
Solutions
1. Evaluate the exact value of each logarithm (dont use a calculator!)
(a) log4 64 = 3
1
(b) log7 49 = 2
2
(c) loge ex = x2
2. Find an exact solution to the equation
log2 x4 log2 x = 7
The rst goal here is to
Math 122 ESP
Trigonometry Three
Spring 2014
1. Solve the following trigonometric equations on the interval 0 < 2.
(a) sin(3 + /18) = 1 First, 0 < 2 when /18 3 + /18 < 6 + /18, so we nd solutions
to sin(x) = 1 on the interval [/18, 6 + /18). Since sin(x) =
Math 122 ESP
Polynomial and Rational Functions
Spring 2014
1. Use a calculator to graph these in the standard viewing window (that is, with 10 x 10 and
10 y 10). Explain why they cannot possibly show a complete graph1 . Find a window that does
show a comp
Functions
Math 122 ESP
Spring 2014
Solutions
1. Below is a list of some simple algebra problems. Some of the solutions are correct and some of them
are wrong! For each problem:
(a) determine if the answer is correct;
(b) determine if there are any mistake
Math 122 ESP
Linear and Quadratic Functions
Spring 2014
1. Find the slope and y-intercept of the line joining the given pair of points, then graph the line, and
determine if it the function is increasing, decreasing, or constant.
(a) (2, 5) and (1, 3)
Thi
Trigonometric Functions
Math 122 ESP
Spring 2014
1. What is 1 radian? What is 1 degree?
One degree is the amount of angle it takes to turn 1/360 around a circle. One radian is the amount of
angle covered by going 1 radius around the circumference of a cir