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

Determining the domain and range of a function as well as intervals where it's increasing, decreasing, and/or constant

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 a function is not 1-1

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

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