5 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.

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…