functions 153 videos

Derivatives of Exponential Functions
Calculus The Derivative
How to use the definition of the derivative to find a derivative formula for exponential functions.
limits derivative definition of the derivative difference quotient exponential functions natural logarithm 
Average Value of a Function
Calculus The Definite Integral
How to find the average value of a function over an interval [a,b].
average value antidifferentiation limits of integration functions area under a curve 
Find an Equation of the Polynomial Function
Precalculus Polynomial and Rational Functions
How we identify the equation of a polynomial function when we are given the intercepts of its graph.
polynomial functions cubic functions x intercepts factors end behavior leading coefficient stretch factor 
Graphing Rational Functions, n>m
Precalculus Polynomial and Rational Functions
How to find the oblique asymptote of a rational function, if it has one.
rational functions polynomials degree horizontal asymptote 
The Tangent Function
Trigonometry Trigonometric Functions
How to define the tangent function for all angles.
tangent right triangle trigonometry the unit circle 
The Tangent Function
Precalculus Trigonometric Functions
How to define the tangent function for all angles.
tangent right triangle trigonometry the unit circle 
Limits of Rational Functions
Precalculus Polynomial and Rational Functions
How to evaluate the limit of k/x^n as x goes to infinity (or negative infinity).
rational functions limits infinity 
Graphing Rational Functions, n=m
Precalculus Polynomial and Rational Functions
How to recognize when a rational function has a horizontal asymptote, and how to find its equation.
rational functions polynomials degree horizontal asymptote 
Graphing Rational Functions, n less than m
Precalculus Polynomial and Rational Functions
How to recognize when y = 0 is the horizontal asymptote of a rational function.
rational functions polynomials degree horizontal asymptote 
Finding Zeros of a Polynomial Function
Precalculus Polynomial and Rational Functions
How we find the zeros of a polynomial function in expanded form.
polynomial functions zeros factored form expanded form the factor theorem the rational roots theorem potential zeros synthetic division the reduced polynomial the quadratic formula 
The Chain Rule
Calculus Techniques of Differentiation
How to differentiate a composite function.
composite function composition inside function outside function differentiation 
Chain Rule: The General Power Rule
Calculus Techniques of Differentiation
How to differentiate a composite function when the outside function is a power function.
chain rule composite functions power functions power rule differentiation 
Chain Rule: The General Exponential Rule
Calculus Techniques of Differentiation
How to differentiate a composite function when the outside function is exponential.
chain rule composite functions composition exponential functions 
Proving Two Functions are Inverses
Algebra 2 Inverse, Exponential and Logarithmic Functions
How to use algebra to show that two functions are inverses.
proving inverses composition 
Tricky Substitutions Involving Radicals
Calculus Antiderivatives and Differential Equations
How to antidifferentiate functions with radicals.
substitution antidifferentiation radical functions 
Evaluating Limits Algebraically, Part 1
Calculus Limits and Continuity
How to evaluate the limit of a function using continuity.
limits definition of continuous function domain of a function rational functions 
The Reciprocal Trigonometric Functions
Precalculus Trigonometric Functions
How to define the reciprocal trigonometric functions, the reciprocal identities, and the Pythagorean identities.
identities the unit circle reciprocal identities the Pythagorean identities 
Derivatives of Logarithmic Functions
Calculus The Derivative
How to infer the derivative of the natural log function using a calculator investigation.
derivative formula limits derivative the number e numerical approximation of the derivative natural logarithm