Section 6.1 Angle Measure
An angle AOB consists of two rays R1 and R2 with a common vertex O (see the Figures
below). We often interpret an angle as a rotation of the ray R1 onto R2 . In this case, R1
Section 6.3 Trigonometric Functions of Angles
In the preceding section we defined the trigonometric ratios for acute angles. Here we extend
the trigonometric ratios to all angles by defining the trigo
Section 6.2 Trigonometry of Right Triangles
Trigonometric Ratios
Since any two right triangles with angle are similar, the trigonometric ratios are the same,
regardless of the size of the triangle; th
Section 6.6 The Law of Cosines
The Law of Sines cannot be used directly to solve triangles if we know two sides and the angle
between them or if we know all three sides (these are Cases 3 and 4 of the
Section 6.5 The Law of Sines
To solve a triangle, we need to know certain information about its sides and angles. A triangle
is determined by three of its six parts (angles and sides) as long as at le
Section 3.4 Real Zeros of Polynomials
Rational Zeros of Polynomials
To help us understand the next theorem, lets consider the polynomial
P (x) = (x 2)(x 3)(x + 4) = x3 x2 14x + 24
From the factored fo
Section 10.2 Systems of Linear Equations in Several Variables
EXAMPLE: Find all solutions of the system
x+y+z =1
y+z =1
2z = 4
Solution 1(Substitution Method): We solve for z in the last equation.
2z
Section 1.6 Modeling with Equations
EXAMPLE: A car rental company charges $30 a day and 15c a mile for renting a car. Helen
rents a car for two days and her bill comes to $108. How many miles did she
Section 8.4 Plane Curves and Parametric Equations
Suppose that x and y are both given as functions of a third variable t (called a parameter) by the
equations
x = f (t),
y = g(t)
(called parametric eq
Section 1.10 Lines
The Slope of a Line
EXAMPLE: Find the slope of the line that passes through the points P (2, 1) and Q(8, 5).
Solution: We have
m=
y2 y1
4
2
51
= =
=
x2 x1
82
6
3
1
EXAMPLE: Find the
Section 1.7 Inequalities
Linear Inequalities
An inequality is linear if each term is constant or a multiple of the variable.
EXAMPLE: Solve the inequality 3x < 9x + 4 and sketch the solution set.
Solu
Section 2.2 Graphs of Functions
DEFINITION: A function f is a rule that assigns to each element x in a set A exactly one
element, called f (x), in a set B. Its graph is the set of ordered pairs
cfw_(x
Mathematical Functions - Fall 2012
Quiz 1, September 16, 2012
In the following problems you are required to show all your work and provide the necessary explanations everywhere to get full credit.
2 1
Section 3.7 Rational Functions
A rational function is a function of the form
r(x) =
P (x)
Q(x)
where P and Q are polynomials.
Rational Functions and Asymptotes
The domain of a rational function consis
Section 1.8 Coordinate Geometry
The Coordinate Plane
Just as points on a line can be identified with real numbers to form the coordinate line, points
in a plane can be identified with ordered pairs of
Section 2.6 Combining Functions
Sums, Differences, Products, and Quotients
Two functions f and g can be combined to form new functions f + g, f g, f g, and f /g in a
manner similar to the way we add,
Section 3.3 Dividing Polynomials
Long Division of Polynomials
Dividing polynomials is much like the familiar process of dividing numbers. When we divide
38 by 7, the quotient is 5 and the remainder is
Section 2.7 One-to-One Functions and Their Inverses
One-to-One Functions
HORIZONTAL LINE TEST: A function is one-to-one if and only if no horizontal line intersects
its graph more than once.
EXAMPLES:
Section 2.5 Transformations of Functions
Vertical Shifting
EXAMPLE: Use the graph of f (x) = x2 to sketch the graph of each function.
(a) g(x) = x2 + 3
(b) h(x) = x2 2
EXAMPLE: Use the graph of f (x)
Section 10.1 Systems of Linear Equations in Two Variables
EXAMPLE: Find all solutions of the system
2x y = 5
x + 4y = 7
Solution 1(Substitution Method): We solve for x in the second equation.
x + 4y
Section 4.1 Exponential Functions
DEFINITION: An exponential function is a function of the form
f (x) = ax
where a is a positive constant.
1 x
x
10
1 3
-3
= 103 = 1000
10
2
1
-2
= 102 = 100
10
1 1
Section 4.4 Laws of Logarithms
LAWS OF LOGARITHMS: If x and y are positive numbers, then
1. loga (xy) = loga x + loga y.
x
2. loga
= loga x loga y.
y
3. loga (xr ) = r loga x where r is any real num
Section 2.4 Average Rate of Change of a Function
Suppose you take a car trip and record the distance that you travel every few minutes. The
distance s you have traveled is a function of the time t:
s(
Section 4.3 Logarithmic Functions
DEFINITION: Let a be a positive number with a 6= 1. The logarithmic function with base
a, denoted by loga , is defined by
loga x = y
ay = x
So, loga x is the exponent
Mathematical Functions - Fall 2012
Quiz 4 October 7, 2012
This part consists of 4 multiple choice problems. Nothing more than the answer is required; consequently no partial credit will be awarded.
1.
Mathematical Functions - Fall 2012
Quiz 6 November 4, 2012
This part consists of 4 multiple choice problems. Nothing more than the answer is required; consequently no partial credit will be awarded.
1
Mathematical Functions - Fall 2012
Quiz 5 October 14, 2012
This part consists of 4 multiple choice problems. Nothing more than the answer is required; consequently no partial credit will be awarded.
1
Mathematical Functions - Fall 2012
Quiz 3 September 30, 2012
This part consists of 4 multiple choice problems. Nothing more than the answer is required; consequently no partial credit will be awarded.