rational function 179 videos

Optimization Using the Closed Interval Method
Calculus Applications of the Derivative
How to evaluate the limit of a function at points where it is not continuous.

Introduction to Logarithms
Precalculus Exponential and Logarithmic Functions
How to use inverses to define the logarithmic function.
logarithms inverse base exponent logarithmic form exponential form 
Using Synthetic Division to Evaluate Polynomials
Algebra 2 Polynomials
How to use synthetic division to evaluate a function.
evaluating polynomials synthetic division 
Finding an Inverse Graphically
Algebra 2 Inverse, Exponential and Logarithmic Functions
How to graph the inverse of a function using points.
finding an inverse graphically switch x and y flip over y=x 
Introduction to Logarithms
Algebra 2 Inverse, Exponential and Logarithmic Functions
How to use inverses to define the logarithmic function.
logarithms inverse base exponent logarithmic form exponential form 
Exponential Growth and Decay
Precalculus Exponential and Logarithmic Functions
How to find the doubling time of a population when the growth rate is given.
exponential growth exponential functions doubling time logarithmic functions the natural logarithm round off error 
Infinite Limits; Vertical Asymptotes
Calculus Limits and Continuity
How to use onesided limits to find a vertical asymptote.
one sided limits infinity limit does not exist rational functions left hand limit right hand limit table of values numerical approach vertical asymptote 
Graphing the Transformation y = a f(x) + k
Precalculus Introduction to Functions
How to graph the transformation y = a f(x) + k when f(x) = abs(x).
functions transformations stretch compression reflection vertical shift turning point 
The Transformation y = f(bx)
Precalculus Introduction to Functions
How determine what transformation the graph y = f(bx) represents when b > 1.
the square root function horizontal shift horizontal compression compression factor endpoint 
Graphing Radical Equations using Shifts
Algebra Radical Expressions and Equations
How to graph radical functions without making a table of values.
shift dilation 
An Important Limit
Calculus The Derivative
How to interpret the value of a limit important in the derivative of exponential functions.
limits natural logarithm numerical approximation 
Concavity and Inflection Points
Calculus Applications of the Derivative
How to show that a function is discontinuous at a point x=a because it is not defined there.

Economics: Marginal Cost & Revenue
Calculus Applications of the Derivative
How to interpret the derivatives of the cost and revenue functions as marginal cost and marginal revenue.
cost revenue profit marginal cost marginal revenue derivatives of cost and revenue 
Square Root Operations
Geometry Pythagorean Theorem
How to simplify square roots using two different methods.
Pythagorean theorem simplifying square roots adding square roots multiplying square roots rationalizing roots 
Square Root Operations
Trigonometry Pythagorean Theorem
How to simplify square roots using two different methods.
Pythagorean theorem simplifying square roots adding square roots multiplying square roots rationalizing roots 
Parametric Equations and Motion
Precalculus Vectors and Parametric Equations
How to graph a parametric curve, and how to eliminate the parameter to obtain a rectangular equation for the curve.
position time parametric equations path rectangular equation eliminating the parameter square root function direction of motion 
Optimization Using the First Derivative Test
Calculus Applications of the Derivative
How to evaluate the limit of a function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph.

OneSided Limits
Calculus Limits and Continuity
How to use onesided limits to show that a limit does not exist.
one sided limits two sided limits limit does not exist piecewise functions left hand limit right hand limit table of values numerical approach