10 Pre-Calculus Tutorials

These Pre-Calculus tutorials are written by experienced educators, all of whom also offer private tutoring lessons. Get the Pre-Calculus help you need, whether through these tutorials or through private tutoring lessons.

Introduction to imaginary numbers

-Imaginary numbers are represented as i -You will see an imaginary number when there is a negative number within a square root. Imaginary numbers are typically accompanied by an exponent. It is important to understand the rules of exponents before continuing. Before diving into the sample problem, it is important to understand the structure of…

expanding logarithms using the property rules

Before attacking this problem, you should be familiar with these three rules: “b” represents the base 1: Product Rule: -log b (XY) = log b X + log b Y 2: Quotient Rule: -log b (x/y) = log b X – log b Y 3: Power Rule: -log b M^p = p log b M

Finding the Domain of Functions

In this tutorial I will demonstrate the process of finding the domain of a function. The domain of a function is all the allowable values of real numbers that the independent variable (usually x) can be. The restrictions (what we cannot do with real numbers) are 1) Can’t divide by zero. 2) Can’have a negative…

Union & Intersection

Union, denoted by ∪, means the inclusion of ALL elements in a set. Interxection, denoted by ∩, is the inclusion of elements that are the SAME. Easy way to Remember: Union is ALL Elements, pretty easy ? Intersections is finding the same ones. Let’s try an example!

Union & Intersection

Union, denoted by “U”, means the inclusion of ALL elements in a set. Interxection, denoted by “n”, is the inclusion of elements that are the SAME. Easy way to Remember: Union is ALL Elments, pretty easy ? Intersections is finding the same ones. Let’s try an example!

Partial Fraction Decomposition w/ Substitute Numerators

Partial Fraction Decomposition: the process of starting with the simplified answer and taking it back apart, or “decomposing” the final expression into its initial polynomial fractions. With this tutorial, you’ll learn how to set up an equation that will help you to solve problems like these.

5.1 Trig Identities – Reciprocal and Quotient Identities

These identities deal with the reciprocal(s) of the problem given.

Exponential and Logarithmic Equations

Exponential and Logarithmic equations are very simple; however, algebraic mistakes can easily be made. This problem illustrates how to find the solution set in terms of “e” and the solution set in decimal form.

Product Rule for Logarithms

Let’s show that log_a(c*d)=log_a(c) + log_a(d) PROOF: 1. Let log_a(c)=x …. We can name it anything we like 2. Let log_a(d)=y …. Again we can name it anything we like 3. a^x=c and a^y=d … Equivalent exponential forms of the statements in steps 1 and 2. 4. a^x•a^y=c*d .. Reason: If A=B & C=D, then…

Solving for Vertical Asymptotes of Rational Functions

You can tell the function graphed above has a vertical asymptote at x=2 as the graph on the left and right sides of x=2 approach negative infinity and positive infinity, respectively. However, how do we determine the vertical asymptote(s) of a rational function without a graph? In order to find a vertical asymptote of a…

^