College Algebra
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Miscellaneous
Illustration of the ac-method of factoring
Knowing when common factors can be cancelled
Solving a compound linear inequality
Solving a compound linear inequality (example 2)
Solving a quadratic equation by factoring
Solving a quadratic equation by completing the square
Solving a quadratic equation by completing the square (example 2)
Solving a quadratic equation by completing the square (example 3)
Solving a quadratic equation by completing the square (example 4)
Solving a quadratic equation using the quadratic formula
Solving a quadratic equation in nonstandard form using the quadratic formula
Solving a quadratic equation via the quadratic formula
Solving a quartic inequality (part 1)
Solving a quartic inequality (part 2)
Solving a rational inequality (part 1)
Solving a rational inequality (part 2)
Fundamentals of functions
Understanding the concept of a function and how to evaluate a function
Evaluating a function for specified domain values
Understanding how to determine the domain of a function
Understanding how to determine the domain of a function (example 2)
Understanding how to determine the domain of a function (example 3)
Finding the domain of a function algebraically
Graphing a function by plotting points
Graphing a piecewise-defined function
Sketching a graph of a piecewise-defined function
Discussing the vertical line test
Applying the vertical line test to a graph
Sketching a graph of the reciprocal function
Graphing the greatest integer function
Determining the domain and range of a function given its graph
Graphically determining local maximums and local minimums of a function
Calculating the average rate of change of a function on a specified numeric interval
Determining the average rate of change of a function on an interval
Horizontal and vertical shifts of graphs of functions (part 1)
Horizontal and vertical shifts of graphs of functions (part 2)
Reflections of graphs about the axes
Discussing dilations of the graphs of functions
Using transformations to graph a function
Using transformations to graph a function (example 2)
Using transformations (involving reflections) to graph a function
Adding and subtracting functions
Multiplying and dividing functions
Arithmetic of functions (part 1)
Arithmetic of functions (part 2)
Discussing the concept of the composition of two functions
Finding the domain of a composition of functions (part 1)
Finding the domain of a composition of functions (part 2)
Finding the domain of a composition of two functions
Finding the domain of a composition of two functions (another example)
Understanding 1-1 functions and the horizontal line test
Applying the horizontal line test to the graph of a function
Showing that a function is 1-1
Discussing the concept of the inverse of a function
Discussing why only 1-1 functions have inverses
Discussing methods for finding the inverse of a function
Finding the inverse of a function
Explaining how to obtain the graph of the inverse of a function
Graphing the inverse of a function
Exponential and logarithmic functions
Discussing the concept of an exponential function
Basic properties of the graph of an exponential function
Using transformations to graph an exponential function
Finding an exponential function given its graph
Discussing the concept of a logarithm (part 1)
Discussing the concept of a logarithm (part 2)
Determining the graph of a logarithmic function with base a
Converting between exponential form and logarithmic form
Evaluating logarithms (example 2)
Determining the domain of a logarithmic function
Finding a logarithmic function given its graph
Using transformations to graph a logarithmic function
Using the change of base rule to evaluate a logarithm
Explaining the change of base formula
Discussing the laws of logarithms (part 1)
Discussing the laws of logarithms (part 2)
Discussing the laws of logarithms (part 3)
Expanding a logarithmic expression
Expressing a logarithmic expression as a single logarithm
Solving an exponential equation
Solving an exponential equation (example 2)
Solving an exponential equation involving multiple bases
Solving an exponential equation involving two bases (example 2)
Solving a logarithmic equation
Discussing a population growth model
Applying an exponential growth model to a population growth scenario
Applying an exponential growth model to a population growth scenario (example 2)
Discussing an exponential model for radioactive decay
Solving a problem involving an exponential decay model
Applying an exponential decay model to a radioactive decay situation
Discussing Newton's Law of Cooling
An application involving Newton's Law of Cooling
Polynomial and rational functions
Discussing the "end behavior" of the graph of a polynomial function
Graphing a polynomial function in factored form
Graphing a polynomial function in factored form (example 2)
Performing synthetic division of polynomials
Performing synthetic division of polynomials (example 2)
Dividing polynomials using synthetic division
Illustration of the connection between synthetic division and the Remainder Theorem
Determining a polynomial function given its zeros
Determining a polynomial given specified real zeros
Determining all rational zeros of a polynomial
Determining the zeros of a polynomial
Graphing a polynomial function (part 1)
Graphing a polynomial function (part 2)
Determining all zeros (including complex zeros) of a polynomial
Determining a polynomial with complex zeros
Finding a polynomial having complex zeros (another example)
Determining a polynomial having specified complex zeros
Discussing the concept of graphing a rational function
Discussing intercepts of a graph of a rational function
Discussing vertical asymptotes of a graph of a rational function
Discussing horizontal asymptotes of a graph of a rational function
Constructing a graph of a rational function
Graphing a rational function (part 1)
Graphing a rational function (part 2)
Graphing a rational function in factored form
Graphing a rational function in factored form (example 2)
Graphing a rational function having a slant asymptote
Conic sections
Determining the equation of vertical parabola
Determining the equation of a parabola given its vertex and focus
Determining the equation of a shifted parabola
Finding the focus of a shifted parabola whose equation is in expanded form
Graphing a parabola in expanded form
Graphing a shifted horizontal parabola
Graphing a shifted horizontal parabola (example 2)
Sketching a graph of a vertical parabola
Graphing a vertical parabola whose vertex is at the origin
Determining the equation of a vertical ellipse
Finding the equation of a shifted horizontal ellipse
Finding the equation of an ellipse given its vertices and foci
Graphing an ellipse centered at the origin
Sketching a graph of a vertical ellipse
Graphing a shifted vertical ellipse
Finding an equation of a hyperbola given its vertices and foci
Finding the equation of a hyperbola
Finding the equation of a shifted vertical hyperbola
Graphing a horizontal hyperbola
Sketching a graph of a shifted vertical hyperbola