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Brian McLogan
Learning how to identify reflections of multiple functions
π Learn how to identify transformations of functions. Transformation of a function involves alterations to the graph of the parent function. The transformations can be dilations, translations (shifts), reflection, stretches, shrinks,...
Brian McLogan
Setting your quadratic equation equal to zero so that you can factor out GCF and solve
πLearn how to solve a quadratic equation by factoring out the GCF. When factoring out the GCF from an equation we will be looking for what the terms have in common. This method is very useful for quadratic equations that does not have...
Brian McLogan
Showing how to find the inverse of an exponential to find the log, y = 2^x
π Learn how to convert an exponential equation to a logarithmic equation. This is very important to learn because it not only helps us explain the definition of a logarithm but how it is related to the exponential function. Knowing how...
Brian McLogan
Write a geometric sequence in summation notation
π Learn how to write the sum from a geometric series. A series is the sum of the terms of a sequence. A geometric series is the sum of the terms of a geometric sequence. The formula for the sum of n terms of a geometric sequence is given...
Brian McLogan
How to rewrite a logarithm using the change of base formula, log9 (64)
π Learn how to evaluate logarithms using a change of base formula. The change of base formula states that when we have a log of a to the base of b, we can evaluate the logarithm by using a common base for both a and b as follows: log of...
Brian McLogan
Learn how to find the asymptotes of a rational function
π Learn how to find the vertical/horizontal asymptotes of a function. An asymptote is a line that the graph of a function approaches but never touches. The vertical asymptote is a vertical line that the graph of a function approaches but...
Brian McLogan
Explaining the rules of logarithms with examples
π Learn all about the properties of logarithms. The logarithm of a number say a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a). The...
Brian McLogan
How to write a polynomial in standard form
π Learn how to determine the end behavior of the graph of a polynomial function. To do this we will first need to make sure we have the polynomial in standard form with descending powers. We will then identify the leading terms so that...
Brian McLogan
What is the difference between imanginary numbers and complex numbers
In this math tutorial I will show you how write a complex number in standard form after simple operations have been performed. You will learn how to find the value of real and imaginary numbers in a complex number and then write it in...
Brian McLogan
Pre-Calculus - Learn How To Evaluate a Natural Log Using the Rules of Logarithms
π Learn how to evaluate natural logarithms. Recall that the logarithm of a number says a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a)....
Brian McLogan
Pre-Calculus - Using the Properties of Logs to Simplify an Expression
π Learn how to evaluate natural logarithms. Recall that the logarithm of a number says a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a)....
Brian McLogan
Pre-Calculus - Evaluating a Natural Logarithm when Given a Root
π Learn how to evaluate natural logarithms. Recall that the logarithm of a number says a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a)....
Brian McLogan
Pre-Calculus - Evaluate a Simple Log With an Exponent
π Learn how to evaluate basic logarithms. Recall that the logarithm of a number says a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a). Thus,...
Brian McLogan
Pre-Calculus - Evaluating the Difference of Two Logarithms
π Learn how to evaluate logarithm expression. Recall that the logarithm of a number say a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a)....
Brian McLogan
Pre-Calculus - Applying the Properties of Logs to Simplify an Expression
π Learn how to evaluate natural logarithms. Recall that the logarithm of a number says a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a)....
Brian McLogan
Verify an identity by multiplying by the conjugate
π Learn how to verify trigonometric identities having rational expressions. To verify trigonometric expression means to verify that the term(s) on the left hand side of the equality sign is equal to the term(s) on the right hand side. To...
Brian McLogan
Pre-Calculus - Evaluating a Natural Logarithm with a Radical in the Denominator
π Learn how to evaluate natural logarithms. Recall that the logarithm of a number says a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a)....
Brian McLogan
Verifying inverses
π Learn how to show that two functions are inverses. The composition of two functions is using one function as the argument (input) of another function. In simple terms composition of two functions is putting one function inside another...
Brian McLogan
Pre-Calculus - Simplifying the Logarithmic Expression Without a Calculator
π Learn how to evaluate logarithm expression. Recall that the logarithm of a number say a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a)....
Brian McLogan
Add and subtract fractions with unlike denominators for rational expressions
Learn how to add/subtract rational expressions with monomials in the denominator. When adding or subtracting two or more rational expressions with common denominators, we add or subtract only the numerator while we keep the denominator...