Properties of Radical Functions and Expressions Video 2
How to rewrite radical terms as power terms
Problem: Simplify the following expression.
\[\left( \dfrac{2x^{-2}z^5}{3x^4y^{-11}}\right)^{-2}\]
How to rewrite radical terms as power terms
Simplifying an expression with both power and exponential functions using properties of exponents
Explaining how to solve equations with power and exponential terms
Properties of exponents applied to power and exponential expressions
Properties of multiplying and simplifying power and exponential expressions
Properties of exponents applied to power and exponential expressions
Simplifying power and exponential expressions using properties of exponents
Explaining how to solve radical equations and then solving example problems
Solving equations with odd radicals
Solving equations with exponential terms
Solving equations with base e exponential terms
Simplifying power and exponential expressions using properties of exponents
Properties of exponential growth and decay functions
Properties of the exponential function with base e
Solving an equation with exponential functions
Solving an equation with exponential functions
Using the power rule to find derivatives
The definition of higher derivatives and solving an example
Using derivatives to find the velocity and acceleration functions from the position function
Explaining the definition of logarithmic scale and double-log plots
Using logarithms to transform a power function into a linear function
Writing a non-linear function for the graph containing two points on a double-log plot
Writing a non-linear function to represent the line graphed on a semilog plot
Using the second derivative to find the maximum rate of change in a word problem
Simplifying a fraction using properties of exponents
Simplifying a fraction containing fractional exponents
Simplifying a fraction with negative exponents
Determining divergence or convergence of improper integrals
Using the limit definition to find a derivative and proving the power rule
Using the limit definition to find a derivative and proving the power rule
Using implicit differentiation to solve a problem and to prove the power rule for rational exponents
Proving the derivative of ln(x) and the power and product rules using logarithmic differentiation
Determining divergence or convergence of improper integrals
Finding the domain of a function with a denominator, square root, and logarithm
Finding the domain of a function with a natural logarithm and denominator
Finding the domain of a function with a square root in the denominator
Finding the domain of a function with a root and a logarithm in the denominator
Finding the domain of a logarithmic function
Finding the domain of even and odd roots
Finding the domain of functions with even and odd roots
Finding the domain of several rational functions
Finding the domain of a rational function
Explaining how to find any holes and vertical asymptotes of a rational function
Finding the domain of a rational function using factoring
Explaining domain restrictions for denominators, even roots, and logarithms
Explaining the main three forms for linear equations
Discussing properties of linear functions
Discussing the types of linear graphs including horizontal and vertical lines and their properties
Discussing how to write the equation of a line through two given points
Writing a linear equation of profit from a business word problem
Solving a linear equation algebraically and showing how this relates to the graph
Solving a linear equation algebraically
Solving a linear equation algebraically and showing how this relates to the graph
Explaining the format and possible solutions for a system of two linear equations
Solving a system of linear equations with two variables
Solving a system of two linear equations with two variables using the elimination method
Solving a system of two linear equations using a TI-84 calculator
Solving a system of two linear equations using a TI-84 calculator
Solving a system of two linear equations using a TI-84 calculator
Explaining the standard form for a quadratic equation and the possible number of solutions
Solving quadratic equations with the difference of two squares formula
Solving quadratic equations by factoring
Solving a quadratic equation by factoring
Solving a quadratic equation by factoring
Solving quadratic equations with the quadratic formula and discussing the number of possible solutions
Explaining when a quadratic equation does not have a real solution
Explaining the graph and properties for the parent function of quadratics
Discussing properties of quadratic functions including the vertex, domain, range, and end behavior
Solving equations with multiple radicals
Explaining the general properties of even and odd root functions
Solving equations with even roots and checking the solutions
Explaining the terminology and rules of logarithms
Explaining the basic properties of logarithmic functions
Expanding logarithmic expressions using logarithm rules
Condensing a logarithmic expression into a single logarithm
Explaining how to solve logarithmic equations
Solving logarithmic equations with a single logarithm term
Solving logarithmic equations with multiple logarithm terms
Solving logarithmic equations with multiple logarithm terms on both sides
Discussing parent functions of rational functions and their properties
Finding horizontal asymptotes for rational functions
Explaining how to do polynomial long division
Finding horizontal asymptotes for rational functions
Determining the end behavior and horizontal asymptotes for rational functions
Explaining basic algebraic operations for fractions
How to simplify rational expressions
Adding and subtracting rational expressions by finding a common denominator
Explaining how to multiply and divide rational expressions
Performing algebraic operations with rational expressions and simplifying the answer
Solving equations that contain rational expressions
Solving an equation that contains rational expressions
Solving an equation that contains rational expressions
Explaining the format and possible solutions for a system of two linear equations