MA 115 030 PRECALCULUS
HOMEWORK 2
WING HONG TONY WONG
When you work on these homework problems, please do not simply write down the numerical answers, but also the step-by-step deduction for each problem. When I grade
your quizzes, tests and nal exam, you
MA 115 030 PRECALCULUS
HOMEWORK 1
WING HONG TONY WONG
When you work on these homework problems, please do not simply write down the numerical answers, but also the step-by-step deduction for each problem. When I grade
your quizzes, tests and nal exam, you
MA 115 030 PRECALCULUS
LECTURE 1
WING HONG TONY WONG
Review in polynomials, exponents and radicals
This lecture is related to Sections R.1, R.4, R.5 and 1.1.
N
Z
Q
R
R\Q
natural numbers
integers
rational numbers
real numbers
irrational numbers
an element
MA 115 030 PRECALCULUS
LECTURE 6
WING HONG TONY WONG
1.2 Relations and functions, domain and range
Last lecture, we discussed what a function is, using the set theoretic way. We also discussed how to nd the dening expression for a function, if the functio
MA 115 030 PRECALCULUS
LECTURE 7
WING HONG TONY WONG
1.3 Linear functions
Last lecture, we started discussing about linear functions and how the graphs of linear
functions form a straight line on the rectangular coordinate plane.
The equation y = mx + c i
MA 115 030 PRECALCULUS
LECTURE 5
WING HONG TONY WONG
1.2 Relations and functions, domain and range
A relation is a set of ordered pairs of real numbers. It can be a nite set, e.g. cfw_(1, 2), (2, 5),
(2, ), (3, 2), or it can be an innite set, e.g. cfw_(x,
MA 115 030 PRECALCULUS
LECTURE 4
WING HONG TONY WONG
Last lecture, we nished reviewing the procedures in simplifying radicals, and discussed
about rectangular coordinate systems.
1.2 Intervals and set notation
On the real line, we often need to refer to a
MA 115 030 PRECALCULUS
LECTURE 2
WING HONG TONY WONG
Review in polynomials, exponents and radicals
This lecture is related to Sections R.1, R.4, R.5 and 1.1.
Last lecture, we reviewed about integer exponents, polynomials of one and several variables. To c
MA 115 030 PRECALCULUS
LECTURE 3
WING HONG TONY WONG
R.5 Review in radicals
Last lecture, we reviewed the denitions of radicals, and gave some rules in simplifying
radical expressions.
To simplify radical expressions, we have the following rules.
The radi
MA 115 030 PRECALCULUS
LECTURE 8
WING HONG TONY WONG
Last lecture, we nished discussing the dierent forms of equations of lines, including
slope-intercept form, point-slope form and two point form. We also talked about how the
slopes of parallel lines and
MA 115 030 PRECALCULUS
LECTURE 9
WING HONG TONY WONG
Last lecture, we nished discussing how to solve linear equations, including the traditional
way, as well as the graphical approach. Just make sure we know how to simply fractions,
since many students te
MAT 115 030 PRECALCULUS
LECTURE 16
WING HONG TONY WONG
2.4 Absolute value functions
|f (x)| =
f (x)
if x 0
.
f (x) if x < 0
Hence, whenever f (x) drops below the x-axis, we reect that portion across the x-axis so
that the whole graph of y = |f (x)| sits a
MAT 115 030 PRECALCULUS
LECTURE 20
WING HONG TONY WONG
3.1 Complex numbers
To solve a wider range of equations, the number system is extended several times, from
natural numbers, to natural numbers including zero, to integers, to fractions, to irrational
MAT 115 030 PRECALCULUS
LECTURE 15
WING HONG TONY WONG
2.3 Stretching, shrinking, and reecting graphs
Example 1. What are the graphs of f (x) =
3
and f (x) = 2 ( x 1)?
Example 2. What are the graphs of f (x) =
and f (x) = 3 ( x 1)?
8
1
x 1, f (x) = 1 ( x
MAT 115 030 PRECALCULUS
LECTURE 13
WING HONG TONY WONG
Last lecture, we discussed about even and odd functions, which are related to function
symmetries.
2.2 Vertical and horizontal shifts of graphs
Example 1. What are the graphs of f (x) = x2 , f (x) = x
MA 115 030 PRECALCULUS
LECTURE 10
WING HONG TONY WONG
Last lecture, we nished discussing how to solve linear inequalities.
2.1 Graphs of basic functions and relations
The following denitions are just the simplied versions of what actual mathematicians
use
MA 115 030 PRECALCULUS
LECTURE 11
WING HONG TONY WONG
Last lecture, we started the discussions about continuous, increasing and decreasing functions.
2.1 Graphs of basic functions and relations
if x < 0
x
1
if x = 0 is continuous on (, 0) as well as on
Ex