4/16/2018 Mat 175 Professor Gebuza
Final Exam Study Guide
Chapter 1, sections XXXXXXXXXX
Graphs and solutions of equations and functions:
o x and y intercepts, domain and range
Distance and midpoint between two points
o Equation of a circle: center and radius
Linear functions:
o Slope, zeros
o Slope-intercept and point-slope equation
o Vertical, horizontal, parallel and perpendicular lines
o Applications of slope: Average Rate of Change
Solving equations and inequalities in one variable
Chapter 2, sections XXXXXXXXXX
Increasing, decreasing and constant functions
Relative maxima and minima
Piecewise functions
Composition of functions
Symmetry with respect to x, y-axis and origin (even and odd functions)
Transformations of graphs:
o Vertical and horizontal translations of graphs
o Reflections across x-axis and y-axis
o Vertical and horizontal stretching and shrinking
Direct and indirect variation: variation constant and equation of variation
Chapter 3, sections XXXXXXXXXX
Complex numbers in a + bi form
Addition, subtraction and multiplication of complex numbers
Solving quadratic equations:
o Principle of Zero products and Square Roots
o Completing the Square and Quadratic Formula
o Discriminant of the quadratic equation
4/16/2018 Mat 175 Professor Gebuza
Final Exam Study Guide
Graphing quadratic functions:
o Vertex, axis of symmetry, minimum and maximum values, domain
and range, intervals on which quadratic function increases/decreases
Solving rational and radical equations
Solving equations and inequalities with absolute value
Chapter 4, section 4.1 & 4.2
Polynomial functions: leading term, leading coefficient & degree of function
Leading term test
Zeros of polynomial functions, Multiplicity and Intermediate Value theorem
Graphing polynomial functions
Chapter 9, section 9.1
Solving system of equations graphically, using the substitution or
elimination method
Chapter 6, sections XXXXXXXXXX
Trigonometric functions of acute angles in right triangle:
o Reciprocal functions
o Trigonometric functions of 45, 30 & 60 degree angles
o Cofunction identities
Angle measure in DMS form
Solving a right triangle:
o Application problems: angle of elevation, angle of depression,
earing
Trigonometric functions of any angle:
o Positive and negative rotation, coterminal angles, complimentary and
supplementary angles, reference angle
Unit circle:
o Angle measure in radians
o Converting between degree and radian (radian & degree) measures
o Angular and linear speeds
4/16/2018 Mat 175 Professor Gebuza
Final Exam Study Guide
Trigonometric functions using a unit circle:
o Reflections on a unit circle
Graphs of trigonometric functions:
o Domain and range, period, amplitude
o Odd and even trigonometric functions
Transformations of Sine and Cosine functions:
o Vertical and horizontal shift
o Vertical and horizontal stretching or shrinking
o Reflections across x and y-axis
o Combined transformations
Note: Anything covered in class, in Blackboard, in the homework, or in the
textbook is eligible for the exam. However, the above topics represent the
major part of the exam.