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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,

bearing

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.

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,

bearing

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.

Answered 2 days AfterMay 09, 2021

83622 assignment

Substitute (1,-4) in the equation

Left side = 2(1)-(-4) = 6 equals right side

Hence true.

Keep y on one side and others on next side

2x-y = 6

-y = -2x+6...

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