# Math 141 Videos of Selected Topics

Topic |
Video |
Notes |

Difference Quotients | Video | Notes |

Domain and Range – Intermediate | Video | Notes |

Ellipses | Video | Notes |

Exponentials and Logarithms – Advanced | Video | Notes |

Factoring Special Forms – Advanced | Video | Notes |

Factoring Trinomials – Advanced | Video | Notes |

Hyperbolas | Video | Notes |

Parabolas for College Algebra | Video | Notes |

Partial Fraction Decomposition | Video | Notes |

Piecewise-Defined Functions | Video | Notes |

**Math 141 Lecture Videos**

Each of these links send you to a play list of the videos for that chapter. The videos are listed both by section number and topic.

## Chapter R Videos — This chapter covers:

- union, intersection, complement of sets
- subsets of the real numbers
- properties of the real numbers
- domain
- laws of exponents
- geometry formulas
- add, subtract, multiply and divide polynomials
- synthetic division
- special products
- factoring difference between squares and trinomials
- factor by grouping
- factor by factoring out binomial factors
- completing the square
- add, subtract, multiply and divide rational expressions
- simplify complex rational expressions
- simplify radicals
- simplify expressions with rational exponents

## Chapter 1 Videos — This chapter covers:

- solve linear and rational equations
- solve quadratic equations
- use the discriminant to determine the number and type of solutions
- solve radical equations
- learn about extraneous solutions
- learn how to write the solution to an inequality in interval notation
- solve linear inequalities
- solve absolute value equations and inequalities
- mixture word problems
- distance, rate, time word problems
- investment word problems
- perimeter, area and other geometry word problems
- work rate word problems

## Chapter 2 Videos — This chapter covers:

- distance and midpoint formulas
- graphing techniques
- intercepts of a graph
- graphing a line
- finding the equation of a line
- parallel and perpendicular lines
- find the equation of a circle
- graph a circle
- complete the square to put the equation of a circle in standard form
- solve variation problems – direct, inverse and joint

## Chapter 3 Videos — This chapter covers:

- definition of a function
- domain
- difference quotient
- graph basic functions
- determine if a function is even, odd or neither
- locate local minima and maxima of a graph
- determine when a graph is increasing, decreasing or constant
- find average rate of change
- find the equation of the secant line
- graph a function using transformations:
- graph parent function
- multiply or divide x or y coordinates (if needed) then move up, down, right or left (if needed)
- come up with an equation that models a real life situation
- write one variable as a function of another variable

## Chapter 4 Videos — This chapter covers:

- determine the average rate of change (slope) of a line
- solve linear application problems
- complete the square to put a quadratic function in standard form – often called vertex form
- determine the vertex of a quadratic function using x= -b/(2a)
- determine the maximum or minimum of a quadratic function without graphing
- use quadratic models to solve real life situations
- solve quadratic inequalities

## Chapter 5 Videos — This chapter covers:

- graph a monomial function
- find zeros and multiplicities of a polynomial
- use the leading term to determine the end behavior of the graph of a polynomial function
- graph a polynomial using it’s leading term, zeros and their multiplicities
- determine where a rational function will have hole, x-intercepts, and vertical asymptotes
- determine the horizontal or slant asymptote of a rational function
- use a sign graph as an aid in graphing a function
- domain of a function
- graphing rational functions near different types of asymptotes
- solve polynomial and rational inequalities
- use of the Remainder Theorem to determine other zeros of a function
- use of the Intermediate Value Theorem to help in determining zeros of a function
- use of the Rational Zero Test to find the possible rational zeros of a function
- find the real zeros of a polynomial function
- find the complex zeros of a polynomial function
- find a function with known zeros

## Chapter 6 Videos — This chapter covers:

- find the composition of functions
- find the inverse of a function
- graph an exponential function
- graph a logarithmic function
- work with properties of logarithms
- solve exponential and logarithmic equations
- find the domain of a logarithmic function

## Chapter 7 Videos — This chapter covers:

- graph a parabola
- find the directrix, focus and latus rectum of a parabola
- graph an ellipse
- find the foci of an ellipse
- graph a hyperbola
- find the foci, and equations of the asymptotes of a hyperbola
- complete the square to change the equation of a conic section from general form to standard form
- derive the equation of a conic section

## Chapter 8 Videos — This chapter covers:

- solve a system of linear equations
- find the partial fraction decomposition for a rational expression
- solve a system of nonlinear equations

## Chapter 9 Videos — This chapter covers:

- find the terms of a sequence
- determine the formula for a sequence or series
- find the value of a series
- recognize arithmetic and geometric sequences and series
- prove statements using mathematical induction
- use the binomial theorem to expand a power of a binomial
- use the binomial theorem to find a specific term in the expansion of the power of a binomial